%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL108-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 02:00:57 PM UTC 2026
% Result : Unsatisfiable 5.31s 1.19s
% Output : Proof 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 4
% Syntax : Number of formulae : 147 ( 143 unt; 0 def)
% Number of atoms : 155 ( 134 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 561 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f0_nnf,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t5,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(f1,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(U,V),equivalent(equivalent(equivalent(W,V),equivalent(W,U)),V6))),equivalent(Z,equivalent(equivalent(Y,X),V6)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_27_1690) ).
fof(f1_nnf,plain,
! [X,Y,Z,U,V,W,V6] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(U,V),equivalent(equivalent(equivalent(W,V),equivalent(W,U)),V6))),equivalent(Z,equivalent(equivalent(Y,X),V6)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U,V,W,V6] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(U,V),equivalent(equivalent(equivalent(W,V),equivalent(W,U)),V6))),equivalent(Z,equivalent(equivalent(Y,X),V6)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(equivalent(X3,X4),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X6))),equivalent(X2,equivalent(equivalent(X1,X0),X6)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X5),equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X7))),equivalent(X3,equivalent(equivalent(X2,X1),X7)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t4,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X5),equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X7))),equivalent(X3,equivalent(equivalent(X2,X1),X7)))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t6,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X5),equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X7)))),true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X1),X7))),true),true),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t6811,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X5),equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X7)))),true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X1),X7))),true),
inference(step,[status(thm)],[t6,t3]) ).
cnf(t9,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X5),equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X7)))),true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X1),X7))),true) = true,
inference(orient,[status(thm)],[t6811]) ).
cnf(t7,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X5),equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X7))),equivalent(X3,equivalent(equivalent(X2,X1),X7))),Y7)),true,ifeq(true,true,is_a_theorem(Y7),true),true),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t6815,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X5),equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X7))),equivalent(X3,equivalent(equivalent(X2,X1),X7))),Y7)),true,is_a_theorem(Y7),true),
inference(step,[status(thm)],[t7,t3]) ).
cnf(t26,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X5),equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X7))),equivalent(X3,equivalent(equivalent(X2,X1),X7))),Y7)),true,is_a_theorem(Y7),true) = true,
inference(orient,[status(thm)],[t6815]) ).
cnf(t10,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X1)),X4)),equivalent(equivalent(equivalent(X5,X6),equivalent(equivalent(X7,X5),equivalent(X7,X6))),X4))),true),
inference(cp,[status(thm)],[t9,t4]) ).
cnf(t6812,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X1)),X4)),equivalent(equivalent(equivalent(X5,X6),equivalent(equivalent(X7,X5),equivalent(X7,X6))),X4))),
inference(step,[status(thm)],[t10,t3]) ).
cnf(t12,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X1)),X4)),equivalent(equivalent(equivalent(X5,X6),equivalent(equivalent(X7,X5),equivalent(X7,X6))),X4))) = true,
inference(orient,[status(thm)],[t6812]) ).
cnf(t16,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(equivalent(equivalent(X4,equivalent(equivalent(X5,X6),equivalent(X5,X7))),equivalent(X4,equivalent(X6,X7))),Y7)),equivalent(equivalent(X2,X3),Y7))),true),
inference(cp,[status(thm)],[t9,t12]) ).
cnf(t6814,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(equivalent(equivalent(X4,equivalent(equivalent(X5,X6),equivalent(X5,X7))),equivalent(X4,equivalent(X6,X7))),Y7)),equivalent(equivalent(X2,X3),Y7))),
inference(step,[status(thm)],[t16,t3]) ).
cnf(t19,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(equivalent(equivalent(X4,equivalent(equivalent(X5,X6),equivalent(X5,X7))),equivalent(X4,equivalent(X6,X7))),Y7)),equivalent(equivalent(X2,X3),Y7))) = true,
inference(orient,[status(thm)],[t6814]) ).
cnf(t27,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4))),equivalent(X1,equivalent(X3,X4))),equivalent(equivalent(equivalent(X5,X6),equivalent(X5,X7)),Y7)),equivalent(equivalent(X6,X7),Y7))),true),
inference(cp,[status(thm)],[t26,t19]) ).
cnf(t6816,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4))),equivalent(X1,equivalent(X3,X4))),equivalent(equivalent(equivalent(X5,X6),equivalent(X5,X7)),Y7)),equivalent(equivalent(X6,X7),Y7))),
inference(step,[status(thm)],[t27,t3]) ).
cnf(t32,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X2,X4))),equivalent(X1,equivalent(X3,X4))),equivalent(equivalent(equivalent(X5,X6),equivalent(X5,X7)),Y7)),equivalent(equivalent(X6,X7),Y7))) = true,
inference(orient,[status(thm)],[t6816]) ).
cnf(t39,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4))),true),
inference(cp,[status(thm)],[t26,t32]) ).
cnf(t6817,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4))),
inference(step,[status(thm)],[t39,t3]) ).
cnf(t41,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4))) = true,
inference(orient,[status(thm)],[t6817]) ).
cnf(t42,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4)),true,is_a_theorem(equivalent(equivalent(X2,X3),X4)),true),true),
inference(cp,[status(thm)],[t5,t41]) ).
cnf(t6818,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4)),true,is_a_theorem(equivalent(equivalent(X2,X3),X4)),true),
inference(step,[status(thm)],[t42,t3]) ).
cnf(t50,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4)),true,is_a_theorem(equivalent(equivalent(X2,X3),X4)),true) = true,
inference(orient,[status(thm)],[t6818]) ).
cnf(t48,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),X5)),equivalent(X1,equivalent(equivalent(X3,X4),X5)))),true),
inference(cp,[status(thm)],[t26,t41]) ).
cnf(t6824,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),X5)),equivalent(X1,equivalent(equivalent(X3,X4),X5)))),
inference(step,[status(thm)],[t48,t3]) ).
cnf(t115,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),X5)),equivalent(X1,equivalent(equivalent(X3,X4),X5)))) = true,
inference(orient,[status(thm)],[t6824]) ).
cnf(t124,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(X2,X4))),X5),equivalent(equivalent(X3,X4),X5))),true),
inference(cp,[status(thm)],[t9,t115]) ).
cnf(t6831,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(X2,X4))),X5),equivalent(equivalent(X3,X4),X5))),
inference(step,[status(thm)],[t124,t3]) ).
cnf(t207,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(X2,X4))),X5),equivalent(equivalent(X3,X4),X5))) = true,
inference(orient,[status(thm)],[t6831]) ).
cnf(t213,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),X4),equivalent(equivalent(X5,X3),equivalent(equivalent(X1,equivalent(X2,X5)),X4)))),true),
inference(cp,[status(thm)],[t50,t207]) ).
cnf(t6834,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),X4),equivalent(equivalent(X5,X3),equivalent(equivalent(X1,equivalent(X2,X5)),X4)))),
inference(step,[status(thm)],[t213,t3]) ).
cnf(t246,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),X4),equivalent(equivalent(X5,X3),equivalent(equivalent(X1,equivalent(X2,X5)),X4)))) = true,
inference(orient,[status(thm)],[t6834]) ).
cnf(t255,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),X1))),true),
inference(cp,[status(thm)],[t9,t246]) ).
cnf(t6835,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),X1))),
inference(step,[status(thm)],[t255,t3]) ).
cnf(t259,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),X1))) = true,
inference(orient,[status(thm)],[t6835]) ).
cnf(t261,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),X1)),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true),
inference(cp,[status(thm)],[t5,t259]) ).
cnf(t6838,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),X1)),X4)),true,is_a_theorem(X4),true),
inference(step,[status(thm)],[t261,t3]) ).
cnf(t318,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),X1)),X4)),true,is_a_theorem(X4),true) = true,
inference(orient,[status(thm)],[t6838]) ).
cnf(t13,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X1)),X4))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X6),equivalent(equivalent(X7,X5),equivalent(X7,X6))),X4)),true),true),
inference(cp,[status(thm)],[t5,t12]) ).
cnf(t6813,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X1)),X4))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X6),equivalent(equivalent(X7,X5),equivalent(X7,X6))),X4)),true),
inference(step,[status(thm)],[t13,t3]) ).
cnf(t18,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X1)),X4))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X6),equivalent(equivalent(X7,X5),equivalent(X7,X6))),X4)),true) = true,
inference(orient,[status(thm)],[t6813]) ).
cnf(t267,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2))),equivalent(X4,X4))),true),
inference(cp,[status(thm)],[t18,t259]) ).
cnf(t6837,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2))),equivalent(X4,X4))),
inference(step,[status(thm)],[t267,t3]) ).
cnf(t303,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2))),equivalent(X4,X4))) = true,
inference(orient,[status(thm)],[t6837]) ).
cnf(t332,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,X1)),true),
inference(cp,[status(thm)],[t318,t303]) ).
cnf(t6839,plain,
true = is_a_theorem(equivalent(X1,X1)),
inference(step,[status(thm)],[t332,t3]) ).
cnf(t359,plain,
is_a_theorem(equivalent(X1,X1)) = true,
inference(orient,[status(thm)],[t6839]) ).
cnf(t361,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(cp,[status(thm)],[t5,t359]) ).
cnf(t6842,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true),
inference(step,[status(thm)],[t361,t3]) ).
cnf(t388,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(orient,[status(thm)],[t6842]) ).
cnf(t51,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,X4)),X5),equivalent(equivalent(X3,equivalent(X1,X4)),X5))),true),
inference(cp,[status(thm)],[t50,t32]) ).
cnf(t6825,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,X4)),X5),equivalent(equivalent(X3,equivalent(X1,X4)),X5))),
inference(step,[status(thm)],[t51,t3]) ).
cnf(t128,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,X4)),X5),equivalent(equivalent(X3,equivalent(X1,X4)),X5))) = true,
inference(orient,[status(thm)],[t6825]) ).
cnf(t393,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(equivalent(X2,X4),X1),equivalent(X4,X3)))),true),
inference(cp,[status(thm)],[t388,t128]) ).
cnf(t6868,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(equivalent(X2,X4),X1),equivalent(X4,X3)))),
inference(step,[status(thm)],[t393,t3]) ).
cnf(t1118,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(equivalent(X2,X4),X1),equivalent(X4,X3)))) = true,
inference(orient,[status(thm)],[t6868]) ).
cnf(t1126,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))),true),
inference(cp,[status(thm)],[t388,t1118]) ).
cnf(t6869,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))),
inference(step,[status(thm)],[t1126,t3]) ).
cnf(t1145,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))) = true,
inference(orient,[status(thm)],[t6869]) ).
cnf(t1146,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(X2,X3)),true),true),
inference(cp,[status(thm)],[t5,t1145]) ).
cnf(t6872,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(X2,X3)),true),
inference(step,[status(thm)],[t1146,t3]) ).
cnf(t1216,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))),true,is_a_theorem(equivalent(X2,X3)),true) = true,
inference(orient,[status(thm)],[t6872]) ).
cnf(t54,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),equivalent(equivalent(X1,X4),X3)))),true),
inference(cp,[status(thm)],[t50,t41]) ).
cnf(t6819,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),equivalent(equivalent(X1,X4),X3)))),
inference(step,[status(thm)],[t54,t3]) ).
cnf(t60,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),equivalent(equivalent(X1,X4),X3)))) = true,
inference(orient,[status(thm)],[t6819]) ).
cnf(t64,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(equivalent(X4,X3),equivalent(X4,X2))))),true),
inference(cp,[status(thm)],[t50,t60]) ).
cnf(t6820,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(equivalent(X4,X3),equivalent(X4,X2))))),
inference(step,[status(thm)],[t64,t3]) ).
cnf(t70,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(equivalent(X4,X3),equivalent(X4,X2))))) = true,
inference(orient,[status(thm)],[t6820]) ).
cnf(t71,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X1),equivalent(equivalent(X4,X3),equivalent(X4,X2)))),true),true),
inference(cp,[status(thm)],[t5,t70]) ).
cnf(t6822,plain,
true = ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X1),equivalent(equivalent(X4,X3),equivalent(X4,X2)))),true),
inference(step,[status(thm)],[t71,t3]) ).
cnf(t92,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X1),equivalent(equivalent(X4,X3),equivalent(X4,X2)))),true) = true,
inference(orient,[status(thm)],[t6822]) ).
cnf(t364,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))),true),
inference(cp,[status(thm)],[t92,t359]) ).
cnf(t6845,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))),
inference(step,[status(thm)],[t364,t3]) ).
cnf(t468,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))) = true,
inference(orient,[status(thm)],[t6845]) ).
cnf(t469,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X1),equivalent(X3,X2))),true),true),
inference(cp,[status(thm)],[t5,t468]) ).
cnf(t6857,plain,
true = ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X1),equivalent(X3,X2))),true),
inference(step,[status(thm)],[t469,t3]) ).
cnf(t802,plain,
ifeq(is_a_theorem(equivalent(X1,X2)),true,is_a_theorem(equivalent(equivalent(X3,X1),equivalent(X3,X2))),true) = true,
inference(orient,[status(thm)],[t6857]) ).
cnf(t319,plain,
true = ifeq(true,true,is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X1))),true),
inference(cp,[status(thm)],[t318,t115]) ).
cnf(t6841,plain,
true = is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X1))),
inference(step,[status(thm)],[t319,t3]) ).
cnf(t372,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X1))) = true,
inference(orient,[status(thm)],[t6841]) ).
cnf(t402,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X1),equivalent(X2,X2))),true),
inference(cp,[status(thm)],[t388,t372]) ).
cnf(t6843,plain,
true = is_a_theorem(equivalent(equivalent(X1,X1),equivalent(X2,X2))),
inference(step,[status(thm)],[t402,t3]) ).
cnf(t426,plain,
is_a_theorem(equivalent(equivalent(X1,X1),equivalent(X2,X2))) = true,
inference(orient,[status(thm)],[t6843]) ).
cnf(t427,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(X2,X2)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t5,t426]) ).
cnf(t6854,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(X2,X2)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t427,t3]) ).
cnf(t719,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,X1),equivalent(X2,X2)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t6854]) ).
cnf(t1131,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X3)),equivalent(X2,X1))),true),
inference(cp,[status(thm)],[t719,t1118]) ).
cnf(t6870,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X3)),equivalent(X2,X1))),
inference(step,[status(thm)],[t1131,t3]) ).
cnf(t1166,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X3)),equivalent(X2,X1))) = true,
inference(orient,[status(thm)],[t6870]) ).
cnf(t1167,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X3))),true,is_a_theorem(equivalent(X2,X1)),true),true),
inference(cp,[status(thm)],[t5,t1166]) ).
cnf(t6876,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X3))),true,is_a_theorem(equivalent(X2,X1)),true),
inference(step,[status(thm)],[t1167,t3]) ).
cnf(t1344,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X3))),true,is_a_theorem(equivalent(X2,X1)),true) = true,
inference(orient,[status(thm)],[t6876]) ).
cnf(t374,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t5,t372]) ).
cnf(t6849,plain,
true = ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3)),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t374,t3]) ).
cnf(t559,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3)),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t6849]) ).
cnf(t1135,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X1)),equivalent(X4,X2)))),true),
inference(cp,[status(thm)],[t50,t1118]) ).
cnf(t6928,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X1)),equivalent(X4,X2)))),
inference(step,[status(thm)],[t1135,t3]) ).
cnf(t2982,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X1)),equivalent(X4,X2)))) = true,
inference(orient,[status(thm)],[t6928]) ).
cnf(t3007,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,equivalent(equivalent(X4,X4),X3)))),true),
inference(cp,[status(thm)],[t559,t2982]) ).
cnf(t6978,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,equivalent(equivalent(X4,X4),X3)))),
inference(step,[status(thm)],[t3007,t3]) ).
cnf(t4739,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,equivalent(equivalent(X4,X4),X3)))) = true,
inference(orient,[status(thm)],[t6978]) ).
cnf(t4763,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X3),X1),X2))),true),
inference(cp,[status(thm)],[t9,t4739]) ).
cnf(t6979,plain,
true = is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X3),X1),X2))),
inference(step,[status(thm)],[t4763,t3]) ).
cnf(t4770,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X3),X1),X2))) = true,
inference(orient,[status(thm)],[t6979]) ).
cnf(t4774,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X2)),true),
inference(cp,[status(thm)],[t1344,t4770]) ).
cnf(t6980,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X2)),
inference(step,[status(thm)],[t4774,t3]) ).
cnf(t4807,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X2)) = true,
inference(orient,[status(thm)],[t6980]) ).
cnf(t4811,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),equivalent(X1,X3))),true),
inference(cp,[status(thm)],[t802,t4807]) ).
cnf(t6984,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),equivalent(X1,X3))),
inference(step,[status(thm)],[t4811,t3]) ).
cnf(t4917,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),equivalent(X1,X3))) = true,
inference(orient,[status(thm)],[t6984]) ).
cnf(t4918,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3))),true,is_a_theorem(equivalent(X1,X3)),true),true),
inference(cp,[status(thm)],[t5,t4917]) ).
cnf(t6991,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3))),true,is_a_theorem(equivalent(X1,X3)),true),
inference(step,[status(thm)],[t4918,t3]) ).
cnf(t5645,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3))),true,is_a_theorem(equivalent(X1,X3)),true) = true,
inference(orient,[status(thm)],[t6991]) ).
cnf(t5649,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),equivalent(X1,X3)),X3)),true),
inference(cp,[status(thm)],[t5645,t1145]) ).
cnf(t6993,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),equivalent(X1,X3)),X3)),
inference(step,[status(thm)],[t5649,t3]) ).
cnf(t6042,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),equivalent(X1,X3)),X3)) = true,
inference(orient,[status(thm)],[t6993]) ).
cnf(t6047,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X3)),true),
inference(cp,[status(thm)],[t1216,t6042]) ).
cnf(t6995,plain,
true = is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X3)),
inference(step,[status(thm)],[t6047,t3]) ).
cnf(t6120,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3)),X3)) = true,
inference(orient,[status(thm)],[t6995]) ).
cnf(t6121,plain,
true = ifeq(true,true,ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3))),true,is_a_theorem(X3),true),true),
inference(cp,[status(thm)],[t5,t6120]) ).
cnf(t6999,plain,
true = ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3))),true,is_a_theorem(X3),true),
inference(step,[status(thm)],[t6121,t3]) ).
cnf(t6615,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X2)),X3))),true,is_a_theorem(X3),true) = true,
inference(orient,[status(thm)],[t6999]) ).
cnf(t134,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,equivalent(X5,X2)),equivalent(equivalent(equivalent(X5,X1),X4),X3)))),true),
inference(cp,[status(thm)],[t50,t128]) ).
cnf(t6832,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,equivalent(X5,X2)),equivalent(equivalent(equivalent(X5,X1),X4),X3)))),
inference(step,[status(thm)],[t134,t3]) ).
cnf(t219,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,equivalent(X5,X2)),equivalent(equivalent(equivalent(X5,X1),X4),X3)))) = true,
inference(orient,[status(thm)],[t6832]) ).
cnf(t6619,plain,
true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)),true),
inference(cp,[status(thm)],[t6615,t219]) ).
cnf(t7000,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)),
inference(step,[status(thm)],[t6619,t3]) ).
cnf(t6769,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)) = true,
inference(orient,[status(thm)],[t7000]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_q_3) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6769]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL108-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 22:00:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.31/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.31/1.19 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------