%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL416-10 : TPTP v9.2.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:40:17 PM UTC 2026
% Result : Unsatisfiable 58.35s 41.21s
% Output : CNFRefutation 58.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 3 RR)
% Number of literals : 42 ( 41 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 187 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(xcb,axiom,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xcb) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(prove_reflexivity,negated_conjecture,
is_a_theorem(equivalent(a,a)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_reflexivity) ).
cnf(c_0_4,axiom,
ifeq(is_a_theorem(equivalent(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
condensed_detachment ).
cnf(c_0_5,axiom,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3))) = true,
xcb ).
cnf(c_0_6,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_7,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).
cnf(c_0_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),equivalent(X5,X4)),X5)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_5]),c_0_6]) ).
cnf(c_0_9,plain,
ifeq(is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).
cnf(c_0_10,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),equivalent(X5,X4)),X5),X6),equivalent(X7,X6)),X7)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_6]) ).
cnf(c_0_11,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),X5),equivalent(X4,X5))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_6]) ).
cnf(c_0_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),equivalent(X5,X4)),X5),X6),X7),equivalent(X6,X7))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_6]) ).
cnf(c_0_13,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(equivalent(equivalent(X2,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),X4)),X1),X5),equivalent(X6,X5)),X6))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_11]),c_0_6]) ).
cnf(c_0_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),X5),equivalent(X4,X5)),X6),equivalent(X7,X6)),X7)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_11]),c_0_6]) ).
cnf(c_0_15,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),equivalent(X5,X4)),X5),X6),X7)),true,is_a_theorem(equivalent(X6,X7)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_12]),c_0_6]) ).
cnf(c_0_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),equivalent(X4,equivalent(equivalent(equivalent(X4,X5),equivalent(X6,X5)),X6))),X7),equivalent(X8,X7)),X8)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_13]),c_0_6]) ).
cnf(c_0_17,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),X5),equivalent(X4,X5)),X6),equivalent(X7,X6))),true,is_a_theorem(X7),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_14]),c_0_6]) ).
cnf(c_0_18,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),X4))),X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_6]) ).
cnf(c_0_19,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),equivalent(X5,X4))),true,is_a_theorem(X5),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_8]),c_0_6]) ).
cnf(c_0_20,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),equivalent(equivalent(equivalent(X4,X5),equivalent(X6,X5)),X6))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_6]) ).
cnf(c_0_21,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_6]) ).
cnf(c_0_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3),equivalent(X4,X3)),X4)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_21]),c_0_6]) ).
cnf(c_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3),X4),equivalent(X3,X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_22]),c_0_6]) ).
cnf(c_0_24,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3),equivalent(X4,X3))),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_22]),c_0_6]) ).
cnf(c_0_25,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),X1),X4),equivalent(X5,X4)),X5))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_23]),c_0_6]) ).
cnf(c_0_26,plain,
ifeq(is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),X4)))),true,is_a_theorem(X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_18]),c_0_6]) ).
cnf(c_0_27,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X4)),X5)),X6),equivalent(X5,X6))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_6]) ).
cnf(c_0_28,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X4)),X5)),equivalent(equivalent(equivalent(X5,X6),equivalent(X7,X6)),X7))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_6]) ).
cnf(c_0_29,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X4)),X1),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_28]),c_0_6]) ).
cnf(c_0_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),X4))),X1),X5),equivalent(X6,X5)),X6)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_6]) ).
cnf(c_0_31,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3),X4)),true,is_a_theorem(equivalent(X3,X4)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_23]),c_0_6]) ).
cnf(c_0_32,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X4)),X1),X2)),X5),equivalent(X6,X5)),X6)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_29]),c_0_6]) ).
cnf(c_0_33,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3),equivalent(X4,X3)),X4),X5),equivalent(X6,X5)),X6)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_22]),c_0_6]) ).
cnf(c_0_34,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),X4))),X1),X5),equivalent(X6,X5))),true,is_a_theorem(X6),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_30]),c_0_6]) ).
cnf(c_0_35,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(equivalent(equivalent(X4,X5),equivalent(X4,X5)),X2),X3))),X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_6]) ).
cnf(c_0_36,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3),equivalent(X4,X3)),X4),X5),equivalent(X6,X5))),true,is_a_theorem(X6),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_33]),c_0_6]) ).
cnf(c_0_37,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X4)),X1),X2)),equivalent(X5,equivalent(equivalent(equivalent(X5,X6),equivalent(X7,X6)),X7)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_6]) ).
cnf(c_0_38,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3),X3)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_6]) ).
cnf(c_0_39,negated_conjecture,
is_a_theorem(equivalent(a,a)) != true,
prove_reflexivity ).
cnf(c_0_40,plain,
is_a_theorem(equivalent(X1,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_6]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL416-10 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 22:33:19 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 58.35/41.21 % Version : CSE_E---1.7
% 58.35/41.21 % Problem : theBenchmark.p
% 58.35/41.21 % SZS status Unsatisfiable for theBenchmark.p
% 58.35/41.21 % SZS output start CNFRefutation
% See solution above
% 58.55/41.42 % Total time : 32.476s
%------------------------------------------------------------------------------