%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG005-1 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 04:03:58 PM UTC 2026
% Result : Unsatisfiable 20.95s 13.06s
% Output : CNFRefutation 21.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 7 RR)
% Number of literals : 55 ( 54 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 136 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(set_difference_1,axiom,
difference(X1,difference(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_1) ).
cnf(set_difference_2,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_2) ).
cnf(set_difference_3,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),difference(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3) ).
cnf(prove_associativity_of_multiply,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
cnf(intersection,axiom,
multiply(X1,X2) = difference(X1,difference(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
cnf(c_0_5,axiom,
difference(X1,difference(X2,X1)) = X1,
set_difference_1 ).
cnf(c_0_6,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
set_difference_2 ).
cnf(c_0_7,plain,
difference(difference(X1,X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),difference(X2,X3)),
set_difference_3 ).
cnf(c_0_9,plain,
difference(X1,X1) = difference(difference(X2,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_5]),c_0_8]) ).
cnf(c_0_10,plain,
difference(difference(X1,X1),difference(X2,X2)) = difference(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_8]),c_0_7]) ).
cnf(c_0_11,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_6,c_0_10]),c_0_10]),c_0_10]),c_0_10]) ).
cnf(c_0_12,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_13,plain,
difference(difference(X1,difference(X2,X3)),X3) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_8]) ).
cnf(c_0_14,plain,
difference(difference(X1,X2),X1) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_15,plain,
difference(X1,difference(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_16,plain,
difference(difference(X1,difference(X2,X3)),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,plain,
difference(difference(X1,X2),difference(X1,difference(X2,X3))) = difference(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_8]),c_0_12]) ).
cnf(c_0_18,plain,
difference(X1,difference(X1,difference(X1,X2))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
difference(X1,difference(X1,difference(difference(X2,X1),X3))) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_5]) ).
cnf(c_0_20,plain,
difference(difference(X1,X2),difference(X3,X1)) = difference(X1,difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_21,plain,
difference(X1,difference(difference(X2,X1),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_5]) ).
cnf(c_0_22,plain,
difference(X1,difference(X2,difference(X3,X1))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_16]) ).
cnf(c_0_23,plain,
difference(difference(difference(X1,X2),X3),X2) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_8]) ).
cnf(c_0_24,plain,
difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_5]) ).
cnf(c_0_25,plain,
difference(difference(difference(X1,X2),X3),X1) = difference(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_12]) ).
cnf(c_0_26,plain,
difference(X1,difference(difference(X2,difference(X3,X1)),X4)) = difference(X1,difference(X2,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_22]) ).
cnf(c_0_27,plain,
difference(difference(X1,difference(X1,X2)),difference(X3,difference(X2,X1))) = difference(difference(X2,X3),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_28,plain,
difference(difference(X1,X2),difference(X3,difference(X4,X1))) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_29,plain,
difference(X1,difference(X1,difference(difference(X1,X2),X3))) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_25]),c_0_15]) ).
cnf(c_0_30,plain,
difference(X1,difference(difference(X1,difference(X1,X2)),X3)) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_6]) ).
cnf(c_0_31,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
prove_associativity_of_multiply ).
cnf(c_0_32,axiom,
multiply(X1,X2) = difference(X1,difference(X1,X2)),
intersection ).
cnf(c_0_33,plain,
difference(difference(X1,difference(X1,X2)),X3) = difference(difference(X2,X3),difference(X2,X1)),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
difference(difference(X1,difference(X1,X2)),X3) = difference(X1,difference(X1,difference(X2,X3))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
difference(difference(X1,difference(X2,X3)),difference(X3,difference(X3,X2))) = difference(difference(X1,X2),difference(X2,X3)),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_36,negated_conjecture,
difference(difference(a,difference(a,b)),difference(difference(a,difference(a,b)),c)) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_37,plain,
difference(X1,difference(X1,difference(X2,X3))) = difference(difference(X2,X3),difference(X2,X1)),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
difference(difference(X1,X2),difference(X1,X3)) = difference(X1,difference(X1,difference(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_34]),c_0_22]) ).
cnf(c_0_39,plain,
difference(difference(X1,difference(X2,X3)),difference(X3,difference(X3,X2))) = difference(X1,X2),
inference(rw,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_40,plain,
difference(difference(X1,difference(X2,X3)),difference(difference(X4,X2),X3)) = difference(difference(X1,difference(X4,X3)),difference(X2,X3)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_41,plain,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_21]),c_0_23]) ).
cnf(c_0_42,negated_conjecture,
difference(c,difference(c,difference(a,difference(a,b)))) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(rw,[status(thm)],[c_0_36,c_0_6]) ).
cnf(c_0_43,plain,
difference(X1,difference(X1,difference(X2,X3))) = difference(X2,difference(X2,difference(X1,X3))),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
difference(X1,difference(X2,difference(X1,difference(X1,X3)))) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_45,plain,
difference(X1,difference(X2,difference(X2,difference(X1,X3)))) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_46,plain,
difference(difference(X1,difference(X2,X3)),difference(X4,difference(X3,difference(X4,X2)))) = difference(difference(X1,difference(X2,X3)),difference(X4,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_5]),c_0_22]),c_0_41]),c_0_22]) ).
cnf(c_0_47,plain,
difference(X1,difference(X2,difference(difference(X3,X1),X4))) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
difference(a,difference(a,difference(c,difference(a,b)))) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
difference(X1,difference(X2,difference(X1,X3))) = difference(X1,difference(X2,difference(X2,X3))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
difference(X1,difference(X2,difference(X1,difference(X2,X3)))) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_46,c_0_5]) ).
cnf(c_0_51,plain,
difference(X1,difference(X2,difference(X3,difference(X4,X1)))) = difference(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_52,negated_conjecture,
difference(a,difference(a,difference(c,difference(a,b)))) != difference(a,difference(a,difference(b,difference(a,c)))),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
difference(X1,difference(X2,difference(X1,X3))) = difference(X1,difference(X3,difference(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_6]),c_0_51]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG005-1 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n011.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 10:13:47 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 20.95/13.06 % Version : CSE_E---1.7
% 20.95/13.06 % Problem : theBenchmark.p
% 20.95/13.06 % SZS status Unsatisfiable for theBenchmark.p
% 20.95/13.06 % SZS output start CNFRefutation
% See solution above
% 21.05/13.14 % Total time : 9.384s
%------------------------------------------------------------------------------