%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG007-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n024.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 04:03:59 PM UTC 2026
% Result : Unsatisfiable 146.10s 107.70s
% Output : CNFRefutation 146.30s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_28)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_set_difference_3,negated_conjecture,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_difference_3) ).
cnf(set_difference_3_simplified,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3_simplified) ).
cnf(set_difference_2,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).
cnf(set_difference_1,axiom,
difference(X1,difference(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
cnf(i_0_4,negated_conjecture,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
prove_set_difference_3,
[final] ).
cnf(i_0_5,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
set_difference_3_simplified,
[final] ).
cnf(i_0_6,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
set_difference_2,
[final] ).
cnf(i_0_7,axiom,
difference(X1,difference(X2,X1)) = X1,
set_difference_1,
[final] ).
cnf(i_0_8,axiom,
X1 = X1 ).
cnf(i_0_9,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_10,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_11,axiom,
( X1 != X2
| difference(X1,X3) = difference(X2,X3) ) ).
cnf(i_0_12,axiom,
( X1 != X2
| difference(X3,X1) = difference(X3,X2) ) ).
cnf(i_0_25,plain,
difference(difference(a,b),difference(X1,difference(a,b))) != difference(a,difference(b,c)),
inference(scs_inference,[],[i_0_18,i_0_13,i_0_11,i_0_12,i_0_9,i_0_10]) ).
cnf(i_0_26,plain,
X1 = difference(X1,difference(X2,X1)),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_37,plain,
difference(X1,difference(X2,difference(X3,X2))) = difference(X1,X2),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_44,plain,
difference(X1,difference(X2,difference(X3,X2))) = difference(X1,X2),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_48,plain,
X1 = difference(X1,difference(X2,X1)),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_91,plain,
X1 = difference(X1,difference(X2,X1)),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_94,plain,
difference(difference(X1,difference(X2,X1)),X3) = difference(X1,X3),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_95,plain,
difference(difference(a,difference(b,c)),c) != difference(difference(a,b),c),
inference(scs_inference,[],[i_0_16,i_0_9]) ).
cnf(i_0_98,plain,
difference(difference(X1,difference(X2,X1)),X3) = difference(X1,X3),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_104,plain,
X1 = difference(X1,difference(X2,X1)),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_121,plain,
difference(difference(X1,difference(X2,X1)),X3) = difference(X1,X3),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_126,plain,
X1 = difference(X1,difference(X2,X1)),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_130,plain,
X1 = difference(X1,difference(X2,X1)),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_143,plain,
X1 = difference(X1,difference(X2,X1)),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_165,plain,
difference(difference(X1,difference(X2,X1)),X3) = difference(X1,X3),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_179,plain,
difference(difference(X1,difference(X2,X1)),X3) = difference(X1,X3),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_184,plain,
difference(X1,difference(X2,difference(X3,X2))) = difference(X1,X2),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_201,plain,
difference(difference(X1,difference(X2,X1)),X3) = difference(X1,X3),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_211,plain,
X1 = difference(X1,difference(X2,X1)),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_29,plain,
difference(difference(b,c),difference(X1,difference(b,c))) != b,
inference(scs_inference,[],[i_0_20,i_0_7,i_0_11,i_0_12,i_0_9]) ).
cnf(i_0_30,plain,
difference(difference(a,difference(X1,a)),difference(b,c)) != difference(a,b),
inference(scs_inference,[],[i_0_24,i_0_22,i_0_20,i_0_7,i_0_11,i_0_12,i_0_9,i_0_10]) ).
cnf(i_0_31,plain,
difference(X1,X2) = difference(difference(X1,difference(X3,X1)),X2),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_41,plain,
difference(X1,X2) = difference(X1,difference(X2,difference(X3,X2))),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_42,plain,
difference(a,difference(b,c)) != difference(difference(a,b),difference(X1,difference(a,b))),
inference(scs_inference,[],[i_0_25,i_0_9]) ).
cnf(i_0_43,plain,
difference(difference(a,b),b) != difference(a,difference(b,c)),
inference(scs_inference,[],[i_0_25,i_0_28,i_0_9,i_0_10]) ).
cnf(i_0_45,plain,
difference(difference(a,b),difference(X1,difference(a,b))) != difference(a,difference(b,c)),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_54,plain,
difference(X1,X2) = difference(difference(X1,difference(X3,X1)),X2),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_57,plain,
difference(X1,X2) = difference(X1,difference(X2,difference(X3,X2))),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_60,plain,
difference(X1,X2) = difference(difference(X1,difference(X3,X1)),X2),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_63,plain,
difference(X1,X2) = difference(X1,difference(X2,difference(X3,X2))),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_69,plain,
difference(X1,X2) = difference(difference(X1,difference(X3,X1)),X2),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_72,plain,
difference(X1,X2) = difference(X1,difference(X2,difference(X3,X2))),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_85,plain,
difference(X1,X2) = difference(difference(X1,difference(X3,X1)),X2),
inference(rename_variables,[],[i_0_22]) ).
cnf(c_0_31,plain,
X1 = difference(X1,difference(X2,X1)),
i_0_26 ).
cnf(c_0_32,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
i_0_6 ).
cnf(c_0_33,plain,
difference(difference(X1,X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_31]) ).
cnf(c_0_34,plain,
difference(difference(X1,X2),difference(X1,X2)) = difference(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_31]) ).
cnf(c_0_35,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
i_0_5 ).
cnf(c_0_36,plain,
difference(X1,X1) = difference(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_34]),c_0_34]),c_0_34]) ).
cnf(c_0_37,plain,
difference(difference(X1,X2),difference(X3,X1)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_38,plain,
difference(difference(X1,X2),difference(X1,X3)) = difference(difference(X3,difference(X3,X1)),X2),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_39,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_33,c_0_36]) ).
cnf(c_0_40,plain,
difference(difference(X1,difference(X2,X3)),difference(X1,X3)) = difference(X3,difference(X3,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
difference(difference(difference(X1,X2),X3),difference(X4,X1)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_42,plain,
difference(difference(X1,X2),X1) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_43,plain,
difference(X1,difference(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_36]),c_0_31]) ).
cnf(c_0_44,plain,
difference(difference(X1,difference(X1,X2)),X3) = difference(X1,difference(X1,difference(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_41]) ).
cnf(c_0_45,plain,
difference(X1,difference(X1,difference(X1,X2))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_42]),c_0_43]) ).
cnf(c_0_46,plain,
difference(difference(X1,X2),difference(difference(X1,X3),X2)) = difference(X3,difference(X3,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_47,plain,
difference(difference(X1,X2),difference(X1,X3)) = difference(X3,difference(X3,difference(X1,X2))),
inference(rw,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_48,plain,
difference(difference(X1,X2),difference(X1,difference(X1,X3))) = difference(difference(X1,X3),X2),
inference(spm,[status(thm)],[c_0_35,c_0_45]) ).
cnf(c_0_49,plain,
difference(X1,difference(X2,difference(X2,X1))) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_32]) ).
cnf(c_0_50,negated_conjecture,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
i_0_4 ).
cnf(c_0_51,plain,
difference(difference(X1,X2),difference(X3,X2)) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_44]),c_0_48]),c_0_49]),c_0_35]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ALG007-1 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 05:14:11 EDT 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.26 % start to proof: theBenchmark
% 146.10/107.70 % Version : CSE_E---1.7
% 146.10/107.70 % Problem : theBenchmark.p
% 146.10/107.70 % SZS status Unsatisfiable for theBenchmark.p
% 146.10/107.70 % SZS output start CNFRefutation
% See solution above
% 146.30/107.96 % Total time : 107.364s
%------------------------------------------------------------------------------