%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:31:51 PM UTC 2026
% Result : Unsatisfiable 7.49s 1.89s
% Output : Proof 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 80
% Number of leaves : 15
% Syntax : Number of formulae : 148 ( 140 unt; 0 def)
% Number of atoms : 156 ( 132 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 1 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-8 aty)
% Number of variables : 93 ( 2 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8))
| ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_2_and_3) ).
fof(f1_nnf,plain,
! [X,Y1,Y4,Y5,Y6,Y7,Y8] :
( achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8))
| ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y1,Y4,Y5,Y6,Y7,Y8] :
( achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8))
| ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( achievable(row(X0),squares(X1,covered,covered,X2,X3,X4,X5,X6))
| ~ achievable(row(X0),squares(X1,not_covered,not_covered,X2,X3,X4,X5,X6)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t33,plain,
ifeq(achievable(row(X1),squares(X2,not_covered,not_covered,X3,X4,X5,X6,X7)),true,achievable(row(X1),squares(X2,covered,covered,X3,X4,X5,X6,X7)),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t243,plain,
ifeq(achievable(row(X1),squares(X2,not_covered,not_covered,X3,X4,X5,X6,X7)),true,achievable(row(X1),squares(X2,covered,covered,X3,X4,X5,X6,X7)),true) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(f7,axiom,
( achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8)))
| ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',place_vertical_pieces) ).
fof(f7_nnf,plain,
! [X,Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8] :
( achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8)))
| ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8] :
( achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8)))
| ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( achievable(row(successor(X0)),squares(complement(X1),complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8)))
| ~ achievable(row(X0),squares(X1,X2,X3,X4,X5,X6,X7,X8)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(achievable(row(X0),squares(X1,X2,X3,X4,X5,X6,X7,X8)),true,achievable(row(successor(X0)),squares(complement(X1),complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8))),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f19,hypothesis,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_row_initially) ).
fof(f19_nnf,plain,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h0,plain,
achievable(row(successor(n1)),squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi19]) ).
cnf(h8,plain,
achievable(row(successor(successor(n1))),squares(complement(complement(not_covered)),complement(complement(removed)),complement(complement(removed)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)),complement(complement(not_covered)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(h17,plain,
achievable(row(successor(successor(successor(n1)))),squares(complement(complement(complement(not_covered))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(not_covered))),complement(complement(complement(not_covered))),complement(complement(complement(not_covered))),complement(complement(complement(not_covered))),complement(complement(complement(not_covered))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h8]) ).
cnf(h25,plain,
achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(complement(not_covered)))),complement(complement(complement(complement(removed)))),complement(complement(complement(complement(removed)))),complement(complement(complement(complement(not_covered)))),complement(complement(complement(complement(not_covered)))),complement(complement(complement(complement(not_covered)))),complement(complement(complement(complement(not_covered)))),complement(complement(complement(complement(not_covered)))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h17]) ).
cnf(h33,plain,
achievable(row(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(removed))))),complement(complement(complement(complement(complement(removed))))),complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(not_covered))))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h25]) ).
cnf(h41,plain,
achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(complement(complement(complement(not_covered)))))),complement(complement(complement(complement(complement(complement(removed)))))),complement(complement(complement(complement(complement(complement(removed)))))),complement(complement(complement(complement(complement(complement(not_covered)))))),complement(complement(complement(complement(complement(complement(not_covered)))))),complement(complement(complement(complement(complement(complement(not_covered)))))),complement(complement(complement(complement(complement(complement(not_covered)))))),complement(complement(complement(complement(complement(complement(not_covered)))))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h33]) ).
cnf(t83,plain,
achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),squares(complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h41]) ).
cnf(f8,axiom,
successor(n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_1_is_2) ).
fof(f8_nnf,plain,
successor(n1) = n2,
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
successor(n1) = n2,
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(t3,plain,
successor(n1) = n2,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t88,plain,
successor(n1) = n2,
inference(orient,[status(thm)],[t3]) ).
cnf(t601,plain,
achievable(row(successor(successor(successor(successor(successor(successor(n2))))))),squares(complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t83,t88]) ).
cnf(f9,axiom,
successor(n2) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_2_is_3) ).
fof(f9_nnf,plain,
successor(n2) = n3,
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
successor(n2) = n3,
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t4,plain,
successor(n2) = n3,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t94,plain,
successor(n2) = n3,
inference(orient,[status(thm)],[t4]) ).
cnf(t602,plain,
achievable(row(successor(successor(successor(successor(successor(n3)))))),squares(complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t601,t94]) ).
cnf(f10,axiom,
successor(n3) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_3_is_4) ).
fof(f10_nnf,plain,
successor(n3) = n4,
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
successor(n3) = n4,
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t5,plain,
successor(n3) = n4,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t89,plain,
successor(n3) = n4,
inference(orient,[status(thm)],[t5]) ).
cnf(t603,plain,
achievable(row(successor(successor(successor(successor(n4))))),squares(complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t602,t89]) ).
cnf(f11,axiom,
successor(n4) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_4_is_5) ).
fof(f11_nnf,plain,
successor(n4) = n5,
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
successor(n4) = n5,
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t6,plain,
successor(n4) = n5,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t90,plain,
successor(n4) = n5,
inference(orient,[status(thm)],[t6]) ).
cnf(t604,plain,
achievable(row(successor(successor(successor(n5)))),squares(complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t603,t90]) ).
cnf(f12,axiom,
successor(n5) = n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_5_is_6) ).
fof(f12_nnf,plain,
successor(n5) = n6,
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
successor(n5) = n6,
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t7,plain,
successor(n5) = n6,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t91,plain,
successor(n5) = n6,
inference(orient,[status(thm)],[t7]) ).
cnf(t605,plain,
achievable(row(successor(successor(n6))),squares(complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t604,t91]) ).
cnf(f13,axiom,
successor(n6) = n7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_6_is_7) ).
fof(f13_nnf,plain,
successor(n6) = n7,
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
successor(n6) = n7,
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(t8,plain,
successor(n6) = n7,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t92,plain,
successor(n6) = n7,
inference(orient,[status(thm)],[t8]) ).
cnf(t606,plain,
achievable(row(successor(n7)),squares(complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t605,t92]) ).
cnf(f14,axiom,
successor(n7) = n8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_7_is_8) ).
fof(f14_nnf,plain,
successor(n7) = n8,
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
successor(n7) = n8,
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(t9,plain,
successor(n7) = n8,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t93,plain,
successor(n7) = n8,
inference(orient,[status(thm)],[t9]) ).
cnf(t607,plain,
achievable(row(n8),squares(complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t606,t93]) ).
cnf(f17,axiom,
complement(not_covered) = covered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_not_covered_is_covered) ).
fof(f17_nnf,plain,
complement(not_covered) = covered,
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
complement(not_covered) = covered,
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t1,plain,
complement(not_covered) = covered,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t85,plain,
complement(not_covered) = covered,
inference(orient,[status(thm)],[t1]) ).
cnf(t608,plain,
achievable(row(n8),squares(complement(complement(complement(complement(complement(complement(covered)))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t607,t85]) ).
cnf(f16,axiom,
complement(covered) = not_covered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_covered_is_not_covered) ).
fof(f16_nnf,plain,
complement(covered) = not_covered,
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
complement(covered) = not_covered,
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t0,plain,
complement(covered) = not_covered,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t86,plain,
complement(covered) = not_covered,
inference(orient,[status(thm)],[t0]) ).
cnf(t609,plain,
achievable(row(n8),squares(complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t608,t86]) ).
cnf(t610,plain,
achievable(row(n8),squares(complement(complement(complement(complement(covered)))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t609,t85]) ).
cnf(t611,plain,
achievable(row(n8),squares(complement(complement(complement(not_covered))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t610,t86]) ).
cnf(t612,plain,
achievable(row(n8),squares(complement(complement(covered)),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t611,t85]) ).
cnf(t613,plain,
achievable(row(n8),squares(complement(not_covered),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t612,t86]) ).
cnf(t614,plain,
achievable(row(n8),squares(covered,complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t613,t85]) ).
cnf(f18,axiom,
complement(removed) = not_covered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_removed_is_not_covered) ).
fof(f18_nnf,plain,
complement(removed) = not_covered,
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
complement(removed) = not_covered,
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t2,plain,
complement(removed) = not_covered,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t87,plain,
complement(removed) = not_covered,
inference(orient,[status(thm)],[t2]) ).
cnf(t615,plain,
achievable(row(n8),squares(covered,complement(complement(complement(complement(complement(complement(not_covered)))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t614,t87]) ).
cnf(t616,plain,
achievable(row(n8),squares(covered,complement(complement(complement(complement(complement(covered))))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t615,t85]) ).
cnf(t617,plain,
achievable(row(n8),squares(covered,complement(complement(complement(complement(not_covered)))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t616,t86]) ).
cnf(t618,plain,
achievable(row(n8),squares(covered,complement(complement(complement(covered))),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t617,t85]) ).
cnf(t619,plain,
achievable(row(n8),squares(covered,complement(complement(not_covered)),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t618,t86]) ).
cnf(t620,plain,
achievable(row(n8),squares(covered,complement(covered),complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t619,t85]) ).
cnf(t621,plain,
achievable(row(n8),squares(covered,not_covered,complement(complement(complement(complement(complement(complement(complement(removed))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t620,t86]) ).
cnf(t622,plain,
achievable(row(n8),squares(covered,not_covered,complement(complement(complement(complement(complement(complement(not_covered)))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t621,t87]) ).
cnf(t623,plain,
achievable(row(n8),squares(covered,not_covered,complement(complement(complement(complement(complement(covered))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t622,t85]) ).
cnf(t624,plain,
achievable(row(n8),squares(covered,not_covered,complement(complement(complement(complement(not_covered)))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t623,t86]) ).
cnf(t625,plain,
achievable(row(n8),squares(covered,not_covered,complement(complement(complement(covered))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t624,t85]) ).
cnf(t626,plain,
achievable(row(n8),squares(covered,not_covered,complement(complement(not_covered)),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t625,t86]) ).
cnf(t627,plain,
achievable(row(n8),squares(covered,not_covered,complement(covered),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t626,t85]) ).
cnf(t628,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t627,t86]) ).
cnf(t629,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,complement(complement(complement(complement(complement(complement(covered)))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t628,t85]) ).
cnf(t630,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t629,t86]) ).
cnf(t631,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,complement(complement(complement(complement(covered)))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t630,t85]) ).
cnf(t632,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,complement(complement(complement(not_covered))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t631,t86]) ).
cnf(t633,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,complement(complement(covered)),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t632,t85]) ).
cnf(t634,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,complement(not_covered),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t633,t86]) ).
cnf(t635,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t634,t85]) ).
cnf(t636,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,complement(complement(complement(complement(complement(complement(covered)))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t635,t85]) ).
cnf(t637,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t636,t86]) ).
cnf(t638,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,complement(complement(complement(complement(covered)))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t637,t85]) ).
cnf(t639,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,complement(complement(complement(not_covered))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t638,t86]) ).
cnf(t640,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,complement(complement(covered)),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t639,t85]) ).
cnf(t641,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,complement(not_covered),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t640,t86]) ).
cnf(t642,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t641,t85]) ).
cnf(t643,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,complement(complement(complement(complement(complement(complement(covered)))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t642,t85]) ).
cnf(t644,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t643,t86]) ).
cnf(t645,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,complement(complement(complement(complement(covered)))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t644,t85]) ).
cnf(t646,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,complement(complement(complement(not_covered))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t645,t86]) ).
cnf(t647,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,complement(complement(covered)),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t646,t85]) ).
cnf(t648,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,complement(not_covered),complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t647,t86]) ).
cnf(t649,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,complement(complement(complement(complement(complement(complement(complement(not_covered))))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t648,t85]) ).
cnf(t650,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,complement(complement(complement(complement(complement(complement(covered)))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t649,t85]) ).
cnf(t651,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,complement(complement(complement(complement(complement(not_covered))))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t650,t86]) ).
cnf(t652,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,complement(complement(complement(complement(covered)))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t651,t85]) ).
cnf(t653,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,complement(complement(complement(not_covered))),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t652,t86]) ).
cnf(t654,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,complement(complement(covered)),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t653,t85]) ).
cnf(t655,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,complement(not_covered),complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t654,t86]) ).
cnf(t656,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,complement(complement(complement(complement(complement(complement(complement(not_covered))))))))) = true,
inference(step,[status(thm)],[t655,t85]) ).
cnf(t657,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,complement(complement(complement(complement(complement(complement(covered)))))))) = true,
inference(step,[status(thm)],[t656,t85]) ).
cnf(t658,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,complement(complement(complement(complement(complement(not_covered))))))) = true,
inference(step,[status(thm)],[t657,t86]) ).
cnf(t659,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,complement(complement(complement(complement(covered)))))) = true,
inference(step,[status(thm)],[t658,t85]) ).
cnf(t660,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,complement(complement(complement(not_covered))))) = true,
inference(step,[status(thm)],[t659,t86]) ).
cnf(t661,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,complement(complement(covered)))) = true,
inference(step,[status(thm)],[t660,t85]) ).
cnf(t662,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,complement(not_covered))) = true,
inference(step,[status(thm)],[t661,t86]) ).
cnf(t663,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered)) = true,
inference(step,[status(thm)],[t662,t85]) ).
cnf(t96,plain,
achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered)) = true,
inference(orient,[status(thm)],[t663]) ).
cnf(t274,plain,
true = ifeq(true,true,achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),true),
inference(cp,[status(thm)],[t243,t96]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t84,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t2747,plain,
true = achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(step,[status(thm)],[t274,t84]) ).
cnf(t595,plain,
achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) = true,
inference(orient,[status(thm)],[t2747]) ).
cnf(f20,negated_conjecture,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_row_8_can_be_covered) ).
fof(f20_nnf,plain,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) != true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t595]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 06:39:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.49/1.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.49/1.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------