%------------------------------------------------------------------------------
% File : SATCoP---0.1
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satcop --statistics %s
% Computer : n029.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 : Mon Sep 7 01:03:11 PM UTC 2026
% Result : Unsatisfiable 50.45s 7.08s
% Output : Proof 51.86s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,plain,
~ sPE(big_V(implies(x,y),implies(y,x)),truth),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_4)]) ).
cnf(g1,plain,
( ~ sPE(truth,big_V(implies(x,y),implies(y,x)))
| sPE(big_V(implies(x,y),implies(y,x)),truth) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g2,plain,
sPE(big_V(implies(x,y),implies(y,x)),implies(implies(implies(x,y),implies(y,x)),implies(y,x))),
inference(ground_cnf,[],[file('Axioms/LCL001-1.ax',big_V_definition)]) ).
cnf(g3,plain,
sPE(implies(implies(x,x),implies(implies(x,x),implies(x,x))),truth),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_2)]) ).
cnf(g4,plain,
sPE(implies(truth,truth),truth),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_1)]) ).
cnf(g5,plain,
sPE(implies(implies(not(x),not(x)),implies(x,x)),truth),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_4)]) ).
cnf(g6,plain,
sPE(implies(truth,big_V(implies(x,y),implies(y,x))),big_V(implies(x,y),implies(y,x))),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_1)]) ).
cnf(g7,plain,
sPE(truth,truth),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g8,plain,
sPE(implies(x,y),implies(x,y)),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g9,plain,
sPE(implies(truth,implies(y,x)),implies(y,x)),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_1)]) ).
cnf(g10,plain,
( ~ ordered(x,implies(x,x))
| ordered(implies(x,x),implies(x,implies(x,x))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2)]) ).
cnf(g11,plain,
( ~ sPE(big_V(implies(x,y),implies(y,x)),implies(implies(implies(x,y),implies(y,x)),implies(y,x)))
| sPE(implies(implies(implies(x,y),implies(y,x)),implies(y,x)),big_V(implies(x,y),implies(y,x))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g12,plain,
sPE(implies(implies(implies(y,x),implies(x,y)),implies(x,y)),implies(implies(implies(x,y),implies(y,x)),implies(y,x))),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_3)]) ).
cnf(g13,plain,
( ~ sPE(truth,implies(truth,big_V(implies(x,y),implies(y,x))))
| ~ sPE(implies(truth,big_V(implies(x,y),implies(y,x))),big_V(implies(x,y),implies(y,x)))
| sPE(truth,big_V(implies(x,y),implies(y,x))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g14,plain,
( ~ sPE(implies(truth,big_V(implies(x,y),implies(y,x))),truth)
| sPE(truth,implies(truth,big_V(implies(x,y),implies(y,x)))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g15,plain,
( ~ ordered(x,truth)
| ordered(implies(x,implies(y,x)),implies(truth,implies(y,x))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1)]) ).
cnf(g16,plain,
sPE(implies(implies(x,y),implies(y,x)),implies(implies(x,y),implies(y,x))),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g17,plain,
sPE(implies(truth,implies(implies(not(x),not(x)),implies(x,x))),implies(implies(not(x),not(x)),implies(x,x))),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_1)]) ).
cnf(g18,plain,
sPE(x,x),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g19,plain,
( ~ sPE(implies(truth,big_V(implies(x,y),implies(y,x))),implies(implies(not(x),not(x)),implies(x,x)))
| ~ sPE(implies(implies(not(x),not(x)),implies(x,x)),truth)
| sPE(implies(truth,big_V(implies(x,y),implies(y,x))),truth) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g20,plain,
( ~ sPE(implies(truth,big_V(implies(x,y),implies(y,x))),implies(truth,implies(implies(not(x),not(x)),implies(x,x))))
| ~ sPE(implies(truth,implies(implies(not(x),not(x)),implies(x,x))),implies(implies(not(x),not(x)),implies(x,x)))
| sPE(implies(truth,big_V(implies(x,y),implies(y,x))),implies(implies(not(x),not(x)),implies(x,x))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g21,plain,
( ~ sPE(implies(truth,implies(implies(not(x),not(x)),implies(x,x))),implies(truth,big_V(implies(x,y),implies(y,x))))
| sPE(implies(truth,big_V(implies(x,y),implies(y,x))),implies(truth,implies(implies(not(x),not(x)),implies(x,x)))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g22,plain,
( ~ sPE(truth,truth)
| ~ sPE(implies(implies(not(x),not(x)),implies(x,x)),big_V(implies(x,y),implies(y,x)))
| sPE(implies(truth,implies(implies(not(x),not(x)),implies(x,x))),implies(truth,big_V(implies(x,y),implies(y,x)))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g23,plain,
( ~ sPE(implies(implies(not(x),not(x)),implies(x,x)),implies(implies(implies(x,y),implies(y,x)),implies(y,x)))
| ~ sPE(implies(implies(implies(x,y),implies(y,x)),implies(y,x)),big_V(implies(x,y),implies(y,x)))
| sPE(implies(implies(not(x),not(x)),implies(x,x)),big_V(implies(x,y),implies(y,x))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g24,plain,
sPE(implies(truth,y),y),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_1)]) ).
cnf(g25,plain,
( ~ sPE(implies(implies(x,y),implies(y,x)),implies(implies(x,y),implies(y,x)))
| ~ sPE(implies(truth,implies(y,x)),implies(y,x))
| sPE(implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))),implies(implies(implies(x,y),implies(y,x)),implies(y,x))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g26,plain,
( ~ sPE(implies(truth,truth),truth)
| ordered(truth,truth) ),
inference(ground_cnf,[],[file('Axioms/LCL001-1.ax',partial_order_definition2)]) ).
cnf(g27,plain,
( ~ ordered(implies(x,x),implies(x,implies(x,x)))
| ordered(x,implies(implies(x,x),implies(x,x))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_2)]) ).
cnf(g28,plain,
sPE(implies(implies(y,x),x),implies(implies(x,y),y)),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_3)]) ).
cnf(g29,plain,
( ~ ordered(truth,truth)
| ordered(implies(x,truth),implies(x,truth)) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2)]) ).
cnf(g30,plain,
sPE(implies(implies(truth,x),x),implies(implies(x,truth),truth)),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_3)]) ).
cnf(g31,plain,
sPE(implies(truth,x),x),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_1)]) ).
cnf(g32,plain,
( ~ sPE(implies(implies(y,x),x),truth)
| ordered(implies(y,x),x) ),
inference(ground_cnf,[],[file('Axioms/LCL001-1.ax',partial_order_definition2)]) ).
cnf(g33,plain,
sPE(implies(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))),implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))),
inference(ground_cnf,[],[file('Axioms/LCL001-0.ax',wajsberg_1)]) ).
cnf(g34,plain,
( ~ ordered(x,truth)
| ordered(implies(x,y),implies(truth,y)) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1)]) ).
cnf(g35,plain,
( ~ sPE(implies(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))),truth)
| sPE(truth,implies(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g36,plain,
( ~ ordered(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))))
| sPE(implies(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))),truth) ),
inference(ground_cnf,[],[file('Axioms/LCL001-1.ax',partial_order_definition1)]) ).
cnf(g37,plain,
( ~ sPE(x,implies(truth,x))
| ~ sPE(x,x)
| sPE(implies(x,x),implies(implies(truth,x),x)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g38,plain,
( ~ sPE(implies(truth,x),x)
| sPE(x,implies(truth,x)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g39,plain,
( ~ ordered(x,implies(implies(implies(x,y),implies(y,x)),implies(y,x)))
| ordered(implies(implies(x,y),implies(y,x)),implies(x,implies(y,x))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_1)]) ).
cnf(g40,plain,
( ~ sPE(x,x)
| ~ sPE(implies(implies(implies(y,x),implies(x,y)),implies(x,y)),implies(implies(implies(x,y),implies(y,x)),implies(y,x)))
| ~ ordered(x,implies(implies(implies(y,x),implies(x,y)),implies(x,y)))
| ordered(x,implies(implies(implies(x,y),implies(y,x)),implies(y,x))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g41,plain,
( ~ ordered(implies(implies(y,x),implies(x,y)),implies(x,implies(x,y)))
| ordered(x,implies(implies(implies(y,x),implies(x,y)),implies(x,y))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_1)]) ).
cnf(g42,plain,
( ~ ordered(x,implies(implies(x,x),implies(x,x)))
| ordered(implies(x,x),implies(x,implies(implies(x,x),implies(x,x)))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2)]) ).
cnf(g43,plain,
( ~ sPE(implies(implies(not(x),not(x)),implies(x,x)),implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))))
| ~ sPE(implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))),implies(implies(implies(x,y),implies(y,x)),implies(y,x)))
| sPE(implies(implies(not(x),not(x)),implies(x,x)),implies(implies(implies(x,y),implies(y,x)),implies(y,x))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g44,plain,
( ~ sPE(implies(implies(not(x),not(x)),implies(x,x)),truth)
| ~ sPE(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))))
| sPE(implies(implies(not(x),not(x)),implies(x,x)),implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g45,plain,
( ~ ordered(implies(x,y),y)
| sPE(implies(implies(x,y),y),truth) ),
inference(ground_cnf,[],[file('Axioms/LCL001-1.ax',partial_order_definition1)]) ).
cnf(g46,plain,
( ~ sPE(implies(x,x),implies(implies(x,truth),truth))
| sPE(implies(implies(x,truth),truth),implies(x,x)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g47,plain,
( ~ sPE(implies(x,x),implies(implies(truth,x),x))
| ~ sPE(implies(implies(truth,x),x),implies(implies(x,truth),truth))
| sPE(implies(x,x),implies(implies(x,truth),truth)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g48,plain,
sPE(implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))),implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g49,plain,
( ~ sPE(truth,implies(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))))
| ~ sPE(implies(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))),implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))))
| sPE(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g50,plain,
( ~ sPE(implies(implies(implies(x,y),implies(y,x)),implies(x,implies(y,x))),truth)
| ~ sPE(implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))),implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))))
| ~ ordered(implies(implies(implies(x,y),implies(y,x)),implies(x,implies(y,x))),implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x))))
| ordered(truth,implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g51,plain,
( ~ ordered(implies(x,implies(y,x)),implies(truth,implies(y,x)))
| ordered(implies(implies(implies(x,y),implies(y,x)),implies(x,implies(y,x))),implies(implies(implies(x,y),implies(y,x)),implies(truth,implies(y,x)))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2)]) ).
cnf(g52,plain,
( ~ ordered(implies(x,truth),implies(x,truth))
| ordered(x,implies(implies(x,truth),truth)) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_1)]) ).
cnf(g53,plain,
( ~ ordered(implies(x,x),implies(x,implies(implies(x,x),implies(x,x))))
| ordered(x,implies(implies(x,x),implies(implies(x,x),implies(x,x)))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_2)]) ).
cnf(g54,plain,
( ~ ordered(implies(y,x),x)
| ordered(implies(implies(y,x),implies(x,y)),implies(x,implies(x,y))) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1)]) ).
cnf(g55,plain,
( ~ sPE(implies(x,y),implies(x,y))
| ~ sPE(implies(truth,y),y)
| ~ ordered(implies(x,y),implies(truth,y))
| ordered(implies(x,y),y) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g56,plain,
( ~ ordered(implies(implies(x,y),implies(y,x)),implies(x,implies(y,x)))
| sPE(implies(implies(implies(x,y),implies(y,x)),implies(x,implies(y,x))),truth) ),
inference(ground_cnf,[],[file('Axioms/LCL001-1.ax',partial_order_definition1)]) ).
cnf(g57,plain,
( ~ sPE(x,x)
| ~ sPE(implies(implies(x,truth),truth),implies(x,x))
| ~ ordered(x,implies(implies(x,truth),truth))
| ordered(x,implies(x,x)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g58,plain,
( ~ sPE(x,x)
| ~ sPE(implies(implies(x,x),implies(implies(x,x),implies(x,x))),truth)
| ~ ordered(x,implies(implies(x,x),implies(implies(x,x),implies(x,x))))
| ordered(x,truth) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g59,plain,
( ~ sPE(implies(implies(y,x),x),implies(implies(x,y),y))
| ~ sPE(implies(implies(x,y),y),truth)
| sPE(implies(implies(y,x),x),truth) ),
inference(ground_cnf,[],[theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : satcop --statistics %s
% 0.10/0.35 % Computer : n029.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 4 19:52:09 UTC 2026
% 0.10/0.35 % CPUTime :
% 50.45/7.08 % symbols: 10
% 50.45/7.08 % clauses: 25
% 50.45/7.08 % start clauses: 1
% 50.45/7.08 % iterative deepening steps: 5156
% 50.45/7.08 % maximum path limit: 16
% 50.45/7.08 % literal attempts: 1389511
% 50.45/7.08 % depth failures: 618911
% 50.45/7.08 % regularity failures: 162314
% 50.45/7.08 % tautology failures: 116164
% 50.45/7.08 % reductions: 0
% 50.45/7.08 % extensions: 1385416
% 50.45/7.08 % SAT variables: 538308
% 50.45/7.08 % SAT clauses: 844511
% 50.45/7.08 % WalkSAT solutions: 844505
% 50.45/7.08 % CDCL solutions: 4
% 50.45/7.08 % SZS status Unsatisfiable for theBenchmark
% 50.45/7.08 % SZS output start ListOfCNF for theBenchmark
% See solution above
%------------------------------------------------------------------------------