%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP025-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n009.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 04:23:35 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.72s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of clauses : 75 ( 35 unt; 18 nHn; 75 RR)
% Number of literals : 134 ( 76 equ; 43 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_and_b_only_members_of_group1,hypothesis,
( X1 = a
| X1 = b
| ~ group_member(X1,g1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_and_b_only_members_of_group1) ).
cnf(d3_member_of_group1,hypothesis,
group_member(d3,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_member_of_group1) ).
cnf(d2_member_of_group1,hypothesis,
group_member(d2,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_member_of_group1) ).
cnf(prove_product_holds_in_group2,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
cnf(b_maps_to_d,hypothesis,
an_isomorphism(b) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_maps_to_d) ).
cnf(d1_member_of_group1,hypothesis,
group_member(d1,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_member_of_group1) ).
cnf(a_maps_to_c,hypothesis,
an_isomorphism(a) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_maps_to_c) ).
cnf(c_times_d_is_d,hypothesis,
product(g2,c,d,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_d_is_d) ).
cnf(d1_times_d2_is_d3,hypothesis,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
cnf(total_function2,axiom,
( X5 = X4
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP006-0.ax',total_function2) ).
cnf(c_times_c_is_c,hypothesis,
product(g2,c,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_c_is_c) ).
cnf(b_times_b_is_a,hypothesis,
product(g1,b,b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_b_is_a) ).
cnf(d_times_d_is_c,hypothesis,
product(g2,d,d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_d_is_c) ).
cnf(a_times_a_is_a,hypothesis,
product(g1,a,a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_a_is_a) ).
cnf(a_times_b_is_b,hypothesis,
product(g1,a,b,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_b) ).
cnf(b_times_a_is_b,hypothesis,
product(g1,b,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_is_b) ).
cnf(d_times_c_is_d,hypothesis,
product(g2,d,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_c_is_d) ).
cnf(c_0_17,hypothesis,
( X1 = a
| X1 = b
| ~ group_member(X1,g1) ),
a_and_b_only_members_of_group1 ).
cnf(c_0_18,hypothesis,
group_member(d3,g1),
d3_member_of_group1 ).
cnf(c_0_19,hypothesis,
( d3 = b
| d3 = a ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,hypothesis,
group_member(d2,g1),
d2_member_of_group1 ).
cnf(c_0_21,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
prove_product_holds_in_group2 ).
cnf(c_0_22,hypothesis,
( d3 = b
| a != b ),
inference(ef,[status(thm)],[c_0_19]) ).
cnf(c_0_23,hypothesis,
an_isomorphism(b) = d,
b_maps_to_d ).
cnf(c_0_24,hypothesis,
( d2 = b
| d2 = a ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( a != b
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),d) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_26,hypothesis,
( d2 = b
| a != b ),
inference(ef,[status(thm)],[c_0_24]) ).
cnf(c_0_27,hypothesis,
group_member(d1,g1),
d1_member_of_group1 ).
cnf(c_0_28,hypothesis,
( a != b
| ~ product(g2,an_isomorphism(d1),d,d) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_29,hypothesis,
( d1 = b
| d1 = a ),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_30,hypothesis,
an_isomorphism(a) = c,
a_maps_to_c ).
cnf(c_0_31,hypothesis,
product(g2,c,d,d),
c_times_d_is_d ).
cnf(c_0_32,hypothesis,
product(g1,d1,d2,d3),
d1_times_d2_is_d3 ).
cnf(c_0_33,hypothesis,
( d1 = b
| a != b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
( d3 = b
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),c) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_30]) ).
cnf(c_0_35,axiom,
( X5 = X4
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X2,X3,X5) ),
total_function2 ).
cnf(c_0_36,hypothesis,
( product(g1,b,d2,d3)
| a != b ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,hypothesis,
( d2 = b
| d3 = b
| ~ product(g2,an_isomorphism(d1),c,c) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_24]),c_0_30]) ).
cnf(c_0_38,hypothesis,
product(g2,c,c,c),
c_times_c_is_c ).
cnf(c_0_39,hypothesis,
( X1 = d3
| a != b
| ~ product(g1,b,d2,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,hypothesis,
( d1 = b
| d3 = b
| d2 = b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_29]),c_0_30]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
( a != b
| ~ product(g2,an_isomorphism(d1),d,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_23]) ).
cnf(c_0_42,hypothesis,
( X1 = d3
| a != b
| ~ product(g1,b,b,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_26]) ).
cnf(c_0_43,hypothesis,
product(g1,b,b,a),
b_times_b_is_a ).
cnf(c_0_44,hypothesis,
( d2 = b
| d1 = b
| product(g1,d1,d2,b) ),
inference(spm,[status(thm)],[c_0_32,c_0_40]) ).
cnf(c_0_45,hypothesis,
( a != b
| ~ product(g2,d,d,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_33]),c_0_23]) ).
cnf(c_0_46,hypothesis,
( d3 = a
| a != b ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,hypothesis,
product(g2,d,d,c),
d_times_d_is_c ).
cnf(c_0_48,hypothesis,
( d1 = b
| d2 = b
| X1 = b
| ~ product(g1,d1,d2,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_49,hypothesis,
a != b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_30]),c_0_47])]) ).
cnf(c_0_50,hypothesis,
( d2 = b
| d1 = b
| X1 = b
| ~ product(g1,d1,a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_24]),c_0_49]) ).
cnf(c_0_51,hypothesis,
( X1 = d3
| ~ product(g1,d1,d2,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_52,hypothesis,
( d1 = b
| d2 = b
| X1 = b
| ~ product(g1,a,a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_29]),c_0_49]) ).
cnf(c_0_53,hypothesis,
product(g1,a,a,a),
a_times_a_is_a ).
cnf(c_0_54,hypothesis,
( d1 = b
| X1 = d3
| ~ product(g1,a,d2,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_29]) ).
cnf(c_0_55,hypothesis,
( d2 = b
| d1 = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( d1 = b
| ~ product(g2,c,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_29]),c_0_30]) ).
cnf(c_0_57,hypothesis,
( d1 = b
| X1 = d3
| ~ product(g1,a,b,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,hypothesis,
product(g1,a,b,b),
a_times_b_is_b ).
cnf(c_0_59,negated_conjecture,
( d1 = b
| ~ product(g2,c,d,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_55]),c_0_23]) ).
cnf(c_0_60,hypothesis,
( d3 = b
| d1 = b ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,hypothesis,
( d2 = b
| X1 = d3
| ~ product(g1,d1,a,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_24]) ).
cnf(c_0_62,negated_conjecture,
d1 = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_23]),c_0_31])]) ).
cnf(c_0_63,negated_conjecture,
( d2 = b
| ~ product(g2,an_isomorphism(d1),c,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_30]) ).
cnf(c_0_64,hypothesis,
( d2 = b
| X1 = d3
| ~ product(g1,b,a,X1) ),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,hypothesis,
product(g1,b,a,b),
b_times_a_is_b ).
cnf(c_0_66,negated_conjecture,
( d2 = b
| ~ product(g2,d,c,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_62]),c_0_23]) ).
cnf(c_0_67,hypothesis,
( d3 = b
| d2 = b ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,hypothesis,
product(g2,d,c,d),
d_times_c_is_d ).
cnf(c_0_69,negated_conjecture,
( d3 = b
| ~ product(g2,d,an_isomorphism(d2),c) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_62]),c_0_23]) ).
cnf(c_0_70,negated_conjecture,
d2 = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_23]),c_0_68])]) ).
cnf(c_0_71,hypothesis,
( X1 = d3
| ~ product(g1,b,d2,X1) ),
inference(rw,[status(thm)],[c_0_51,c_0_62]) ).
cnf(c_0_72,negated_conjecture,
d3 = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_23]),c_0_47])]) ).
cnf(c_0_73,hypothesis,
( X1 = b
| ~ product(g1,b,b,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_70]),c_0_72]) ).
cnf(c_0_74,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_43]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP025-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:17:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.30/1.72 % Version : CSE_E---1.7
% 1.30/1.72 % Problem : theBenchmark.p
% 1.30/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.72 % SZS output start CNFRefutation
% See solution above
% 1.30/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------