%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ039-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Thu Sep 24 02:01:40 PM UTC 2026
% Result : Unsatisfiable 3.25s 0.83s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 20
% Syntax : Number of clauses : 88 ( 34 unt; 0 nHn; 88 RR)
% Number of literals : 142 ( 0 equ; 57 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-12 aty)
% Number of functors : 14 ( 14 usr; 1 con; 0-2 aty)
% Number of variables : 681 ( 33 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(swap_blanks,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X11,X12),e2(X13,X14))
| state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X13,X14),e2(X11,X12)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',swap_blanks) ).
cnf(v4_down,axiom,
( ~ state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12)
| state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',v4_down) ).
cnf(initial_state,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state) ).
cnf(v3_down,axiom,
( ~ state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12)
| state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',v3_down) ).
cnf(v1_down,axiom,
( ~ state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12)
| state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',v1_down) ).
cnf(h_right,axiom,
( ~ state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12)
| state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',h_right) ).
cnf(s1_up,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',s1_up) ).
cnf(s3_up,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',s3_up) ).
cnf(v1_up,axiom,
( ~ state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12)
| state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',v1_up) ).
cnf(s1_left,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',s1_left) ).
cnf(v3_right,axiom,
( ~ state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5)))
| state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',v3_right) ).
cnf(s1_down,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',s1_down) ).
cnf(s3_left,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',s3_left) ).
cnf(s3_down,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',s3_down) ).
cnf(h_left,axiom,
( ~ state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12)
| state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',h_left) ).
cnf(v4_up,axiom,
( ~ state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12)
| state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',v4_up) ).
cnf(s4_right,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(X10,s(X11)),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,s(X11)),e1(X10,X11),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',s4_right) ).
cnf(s2_down,axiom,
( ~ state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(s(X8),X9),X12)
| state(X1,X2,X3,X4,X5,X6,X7,s2(s(X8),X9),X10,X11,e1(X8,X9),X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',s2_down) ).
cnf(v4_left,axiom,
( ~ state(X1,X2,X3,X4,v4(X5,s(X6)),X7,X8,X9,X10,X11,e1(X5,X6),e2(s(X5),X6))
| state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(X5,s(X6)),e2(s(X5),s(X6))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',v4_left) ).
cnf(goal_state,negated_conjecture,
~ state(X1,X2,X3,X4,v4(s(s(o)),s(s(o))),X5,X6,X7,X8,X9,X10,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_state) ).
cnf(c_0_20,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X11,X12),e2(X13,X14))
| state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X13,X14),e2(X11,X12)) ),
inference(fof_simplification,[status(thm)],[swap_blanks]) ).
cnf(c_0_21,plain,
( ~ state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12)
| state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12) ),
inference(fof_simplification,[status(thm)],[v4_down]) ).
cnf(c_0_22,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X11,X12),e2(X13,X14))
| state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X13,X14),e2(X11,X12)) ),
c_0_20 ).
cnf(c_0_23,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
initial_state ).
cnf(c_0_24,plain,
( ~ state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12)
| state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12) ),
c_0_21 ).
cnf(c_0_25,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(s(s(o)))),e2(s(s(s(s(o)))),o)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( ~ state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12)
| state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12) ),
inference(fof_simplification,[status(thm)],[v3_down]) ).
cnf(c_0_27,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(s(o)))),o)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( ~ state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12)
| state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12) ),
inference(fof_simplification,[status(thm)],[v1_down]) ).
cnf(c_0_29,plain,
( ~ state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12)
| state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12) ),
c_0_26 ).
cnf(c_0_30,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(o)),s(s(s(o))))),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_31,plain,
( ~ state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12)
| state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12) ),
c_0_28 ).
cnf(c_0_32,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(o)),s(s(s(o))))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( ~ state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12)
| state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12) ),
inference(fof_simplification,[status(thm)],[h_right]) ).
cnf(c_0_34,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(o)),s(s(s(o))))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( ~ state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12) ),
inference(fof_simplification,[status(thm)],[s1_up]) ).
cnf(c_0_36,plain,
( ~ state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12)
| state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12) ),
c_0_33 ).
cnf(c_0_37,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(o,o)),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_38,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12) ),
inference(fof_simplification,[status(thm)],[s3_up]) ).
cnf(c_0_39,plain,
( ~ state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12) ),
c_0_35 ).
cnf(c_0_40,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(o,o)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12) ),
c_0_38 ).
cnf(c_0_42,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(o)),e2(o,o)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
( ~ state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12)
| state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12) ),
inference(fof_simplification,[status(thm)],[v1_up]) ).
cnf(c_0_44,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(o)),e2(o,o)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( ~ state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12) ),
inference(fof_simplification,[status(thm)],[s1_left]) ).
cnf(c_0_46,plain,
( ~ state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12)
| state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12) ),
c_0_43 ).
cnf(c_0_47,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(s(s(o)))),s(o))),
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_48,plain,
( ~ state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12) ),
c_0_45 ).
cnf(c_0_49,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(o))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
( ~ state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5)))
| state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)) ),
inference(fof_simplification,[status(thm)],[v3_right]) ).
cnf(c_0_51,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(s(s(s(s(o)))),s(o))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
( ~ state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12) ),
inference(fof_simplification,[status(thm)],[s1_down]) ).
cnf(c_0_53,plain,
( ~ state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5)))
| state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)) ),
c_0_50 ).
cnf(c_0_54,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(o)),e2(s(s(s(s(o)))),s(o))),
inference(spm,[status(thm)],[c_0_41,c_0_51]) ).
cnf(c_0_55,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12) ),
inference(fof_simplification,[status(thm)],[s3_left]) ).
cnf(c_0_56,plain,
( ~ state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12)
| state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12) ),
c_0_52 ).
cnf(c_0_57,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(s(s(s(s(o)))),o)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12) ),
c_0_55 ).
cnf(c_0_59,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),o)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(s(s(s(s(o)))),o)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12) ),
inference(fof_simplification,[status(thm)],[s3_down]) ).
cnf(c_0_62,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(o)),s(o))),
inference(spm,[status(thm)],[c_0_22,c_0_60]) ).
cnf(c_0_63,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12) ),
c_0_61 ).
cnf(c_0_64,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(s(s(o)),s(o))),
inference(spm,[status(thm)],[c_0_56,c_0_62]) ).
cnf(c_0_65,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(o)),s(o))),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_66,plain,
( ~ state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12)
| state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12) ),
inference(fof_simplification,[status(thm)],[h_left]) ).
cnf(c_0_67,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(o)),s(o))),
inference(spm,[status(thm)],[c_0_31,c_0_65]) ).
cnf(c_0_68,plain,
( ~ state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12)
| state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12) ),
inference(fof_simplification,[status(thm)],[v4_up]) ).
cnf(c_0_69,plain,
( ~ state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12)
| state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12) ),
c_0_66 ).
cnf(c_0_70,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(o,o)),
inference(spm,[status(thm)],[c_0_22,c_0_67]) ).
cnf(c_0_71,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(X10,s(X11)),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,s(X11)),e1(X10,X11),X12) ),
inference(fof_simplification,[status(thm)],[s4_right]) ).
cnf(c_0_72,plain,
( ~ state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12)
| state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12) ),
c_0_68 ).
cnf(c_0_73,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(o,o)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(s(X8),X9),X12)
| state(X1,X2,X3,X4,X5,X6,X7,s2(s(X8),X9),X10,X11,e1(X8,X9),X12) ),
inference(fof_simplification,[status(thm)],[s2_down]) ).
cnf(c_0_75,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(X10,s(X11)),X12)
| state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,s(X11)),e1(X10,X11),X12) ),
c_0_71 ).
cnf(c_0_76,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(s(s(o)))),e2(o,o)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,plain,
( ~ state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(s(X8),X9),X12)
| state(X1,X2,X3,X4,X5,X6,X7,s2(s(X8),X9),X10,X11,e1(X8,X9),X12) ),
c_0_74 ).
cnf(c_0_78,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(s(o)))),s(s(o))),e2(o,o)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_79,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(o))),s(s(o))),e2(o,o)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_80,hypothesis,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(s(o)))),e1(o,o),e2(s(s(s(o))),s(s(o)))),
inference(spm,[status(thm)],[c_0_22,c_0_79]) ).
cnf(c_0_81,plain,
( ~ state(X1,X2,X3,X4,v4(X5,s(X6)),X7,X8,X9,X10,X11,e1(X5,X6),e2(s(X5),X6))
| state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(X5,s(X6)),e2(s(X5),s(X6))) ),
inference(fof_simplification,[status(thm)],[v4_left]) ).
cnf(c_0_82,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),o),e2(s(s(s(o))),s(s(o)))),
inference(spm,[status(thm)],[c_0_46,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
~ state(X1,X2,X3,X4,v4(s(s(o)),s(s(o))),X5,X6,X7,X8,X9,X10,X11),
inference(fof_simplification,[status(thm)],[goal_state]) ).
cnf(c_0_84,plain,
( ~ state(X1,X2,X3,X4,v4(X5,s(X6)),X7,X8,X9,X10,X11,e1(X5,X6),e2(s(X5),X6))
| state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(X5,s(X6)),e2(s(X5),s(X6))) ),
c_0_81 ).
cnf(c_0_85,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(o))),e2(s(s(s(o))),s(s(o)))),
inference(spm,[status(thm)],[c_0_69,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
~ state(X1,X2,X3,X4,v4(s(s(o)),s(s(o))),X5,X6,X7,X8,X9,X10,X11),
c_0_83 ).
cnf(c_0_87,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PUZ039-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 03:46:07 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.25/0.83 % Version: 3.5.1
% 3.25/0.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.25/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.25/0.83 % Starting new_bool_3 with 300s (1) cores
% 3.25/0.83 % Starting new_bool_1 with 300s (1) cores
% 3.25/0.83 % Starting sh5l with 300s (1) cores
% 3.25/0.83 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1492636 completed with status 0
% 3.25/0.83 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.25/0.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.25/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.25/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.25/0.83 % No SInE strategy applied
% 3.25/0.83 % Search class: FHUNF-FFLF21-MFFFFFNN
% 3.25/0.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.25/0.83 % Starting SubtermCWHack with 136s (1) cores
% 3.25/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.25/0.83 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 154s (1) cores
% 3.25/0.83 % Starting new_bool_3 with 154s (1) cores
% 3.25/0.83 % Starting new_bool_1 with 154s (1) cores
% 3.25/0.83 % G-E--_208_C18_F1_SE_CS_SP_PS_S4d with pid 1492643 completed with status 0
% 3.25/0.83 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4d
% 3.25/0.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.25/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.25/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.25/0.83 % No SInE strategy applied
% 3.25/0.83 % Search class: FHUNF-FFLF21-MFFFFFNN
% 3.25/0.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.25/0.83 % Starting SubtermCWHack with 136s (1) cores
% 3.25/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.25/0.83 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 154s (1) cores
% 3.25/0.83 % Preprocessing time : 0.001 s
% 3.25/0.83 % Presaturation interreduction done
% 3.25/0.83
% 3.25/0.83 % Proof found!
% 3.25/0.83 % SZS status Unsatisfiable
% 3.25/0.83 % SZS output start CNFRefutation
% See solution above
% 3.25/0.83 % Parsed axioms : 43
% 3.25/0.83 % Removed by relevancy pruning/SinE : 0
% 3.25/0.83 % Initial clauses : 43
% 3.25/0.83 % Removed in clause preprocessing : 0
% 3.25/0.83 % Initial clauses in saturation : 43
% 3.25/0.83 % Processed clauses : 2547
% 3.25/0.83 % ...of these trivial : 472
% 3.25/0.83 % ...subsumed : 0
% 3.25/0.83 % ...remaining for further processing : 2075
% 3.25/0.83 % Other redundant clauses eliminated : 0
% 3.25/0.83 % Clauses deleted for lack of memory : 0
% 3.25/0.83 % Backward-subsumed : 0
% 3.25/0.83 % Backward-rewritten : 0
% 3.25/0.83 % Generated clauses : 5462
% 3.25/0.83 % ...of the previous two non-redundant : 2918
% 3.25/0.83 % ...aggressively subsumed : 0
% 3.25/0.83 % Contextual simplify-reflections : 0
% 3.25/0.83 % Paramodulations : 5462
% 3.25/0.83 % Factorizations : 0
% 3.25/0.83 % NegExts : 0
% 3.25/0.83 % Equation resolutions : 0
% 3.25/0.83 % Disequality decompositions : 0
% 3.25/0.83 % Total rewrite steps : 3013
% 3.25/0.83 % ...of those cached : 1251
% 3.25/0.83 % Propositional unsat checks : 0
% 3.25/0.83 % Propositional check models : 0
% 3.25/0.83 % Propositional check unsatisfiable : 0
% 3.25/0.83 % Propositional clauses : 0
% 3.25/0.83 % Propositional clauses after purity: 0
% 3.25/0.83 % Propositional unsat core size : 0
% 3.25/0.83 % Propositional preprocessing time : 0.000
% 3.25/0.83 % Propositional encoding time : 0.000
% 3.25/0.83 % Propositional solver time : 0.000
% 3.25/0.83 % Success case prop preproc time : 0.000
% 3.25/0.83 % Success case prop encoding time : 0.000
% 3.25/0.83 % Success case prop solver time : 0.000
% 3.25/0.83 % Current number of processed clauses : 2032
% 3.25/0.83 % Positive orientable unit clauses : 1990
% 3.25/0.83 % Positive unorientable unit clauses: 0
% 3.25/0.83 % Negative unit clauses : 1
% 3.25/0.83 % Non-unit-clauses : 41
% 3.25/0.83 % Current number of unprocessed clauses: 457
% 3.25/0.83 % ...number of literals in the above : 457
% 3.25/0.83 % Current number of archived formulas : 0
% 3.25/0.83 % Current number of archived clauses : 43
% 3.25/0.83 % Clause-clause subsumption calls (NU) : 1300
% 3.25/0.83 % Rec. Clause-clause subsumption calls : 1300
% 3.25/0.83 % Non-unit clause-clause subsumptions : 0
% 3.25/0.83 % Unit Clause-clause subsumption calls : 0
% 3.25/0.83 % Rewrite failures with RHS unbound : 0
% 3.25/0.83 % BW rewrite match attempts : 1291600
% 3.25/0.83 % BW rewrite match successes : 0
% 3.25/0.83 % Condensation attempts : 0
% 3.25/0.83 % Condensation successes : 0
% 3.25/0.83 % Termbank termtop insertions : 452210
% 3.25/0.83 % Search garbage collected termcells : 85
% 3.25/0.83
% 3.25/0.83 % -------------------------------------------------
% 3.25/0.83 % User time : 0.433 s
% 3.25/0.83 % System time : 0.043 s
% 3.25/0.83 % Total time : 0.476 s
% 3.25/0.83 % Maximum resident set size: 3684 pages
% 3.25/0.83
% 3.25/0.83 % -------------------------------------------------
% 3.25/0.83 % User time : 2.194 s
% 3.25/0.83 % System time : 0.204 s
% 3.25/0.83 % Total time : 2.397 s
% 3.25/0.83 % Maximum resident set size: 4864 pages
% 3.25/0.83 % E exiting
%------------------------------------------------------------------------------