%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG006-1 : 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 : n019.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 1.73s 1.89s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 3 RR)
% Number of literals : 24 ( 23 equ; 2 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(set_difference_1,axiom,
difference(X1,difference(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
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_3,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),difference(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3) ).
cnf(prove_set_difference_3_simplified,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_difference_3_simplified) ).
cnf(c_0_4,axiom,
difference(X1,difference(X2,X1)) = X1,
set_difference_1 ).
cnf(c_0_5,axiom,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
set_difference_2 ).
cnf(c_0_6,plain,
difference(difference(X1,X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_7,axiom,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),difference(X2,X3)),
set_difference_3 ).
cnf(c_0_8,plain,
difference(X1,X1) = difference(difference(X2,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_4]),c_0_7]) ).
cnf(c_0_9,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_8,c_0_8]),c_0_7]),c_0_6]) ).
cnf(c_0_10,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_5,c_0_9]),c_0_9]),c_0_9]),c_0_9]) ).
cnf(c_0_11,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_12,plain,
difference(difference(X1,difference(X2,X3)),X3) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_7]) ).
cnf(c_0_13,plain,
difference(difference(X1,X2),X1) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_14,plain,
difference(X1,difference(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_4,c_0_10]) ).
cnf(c_0_15,plain,
difference(difference(X1,difference(X2,X3)),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,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_13,c_0_15]),c_0_7]),c_0_11]) ).
cnf(c_0_17,plain,
difference(X1,difference(X1,difference(X1,X2))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_13]),c_0_14]) ).
cnf(c_0_18,plain,
difference(X1,difference(X1,difference(difference(X2,X1),X3))) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_4]) ).
cnf(c_0_19,plain,
difference(X1,difference(difference(X2,X1),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_4]) ).
cnf(c_0_20,plain,
difference(difference(difference(X1,X2),X3),X2) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_7]) ).
cnf(c_0_21,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
prove_set_difference_3_simplified ).
cnf(c_0_22,plain,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ALG006-1 : TPTP v9.2.1. Released v2.2.0.
% 0.12/0.13 % 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
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 5 10:14:29 EDT 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % start to proof: theBenchmark
% 1.73/1.89 % Version : CSE_E---1.7
% 1.73/1.89 % Problem : theBenchmark.p
% 1.73/1.89 % SZS status Unsatisfiable for theBenchmark.p
% 1.73/1.89 % SZS output start CNFRefutation
% See solution above
% 1.73/1.89 % Total time : 1.373s
%------------------------------------------------------------------------------