TSTP Solution File: GRP026-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP026-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : Thu Aug 31 00:13:41 EDT 2023
% Result : Unsatisfiable 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 49
% Syntax : Number of formulae : 152 ( 73 unt; 17 typ; 0 def)
% Number of atoms : 267 ( 173 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 178 ( 46 ~; 132 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity_for: $i > $i ).
tff(decl_23,type,
group_member: ( $i * $i ) > $o ).
tff(decl_24,type,
product: ( $i * $i * $i * $i ) > $o ).
tff(decl_25,type,
inverse: ( $i * $i ) > $i ).
tff(decl_26,type,
multiply: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
g1: $i ).
tff(decl_29,type,
b: $i ).
tff(decl_30,type,
c: $i ).
tff(decl_31,type,
f: $i ).
tff(decl_32,type,
g2: $i ).
tff(decl_33,type,
g: $i ).
tff(decl_34,type,
h: $i ).
tff(decl_35,type,
an_isomorphism: $i > $i ).
tff(decl_36,type,
d1: $i ).
tff(decl_37,type,
d2: $i ).
tff(decl_38,type,
d3: $i ).
cnf(all_of_group1,hypothesis,
( X1 = a
| X1 = b
| X1 = c
| ~ group_member(X1,g1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_of_group1) ).
cnf(d3_in_group1,hypothesis,
group_member(d3,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_in_group1) ).
cnf(prove_product_holds_in_group2,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
cnf(a_maps_to_f,hypothesis,
an_isomorphism(a) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_f) ).
cnf(d2_in_group1,hypothesis,
group_member(d2,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_in_group1) ).
cnf(d1_in_group1,hypothesis,
group_member(d1,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_in_group1) ).
cnf(d1_times_d2_is_d3,hypothesis,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
cnf(f_times_f_is_f,hypothesis,
product(g2,f,f,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_f_is_f) ).
cnf(total_function2,axiom,
( X5 = X4
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function2) ).
cnf(total_function1_1,axiom,
( product(X2,X1,X3,multiply(X2,X1,X3))
| ~ group_member(X1,X2)
| ~ group_member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function1_1) ).
cnf(a_times_a_is_a,hypothesis,
product(g1,a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).
cnf(a_in_group1,hypothesis,
group_member(a,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_group1) ).
cnf(c_times_c_is_b,hypothesis,
product(g1,c,c,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_b) ).
cnf(c_maps_to_h,hypothesis,
an_isomorphism(c) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_maps_to_h) ).
cnf(c_in_group1,hypothesis,
group_member(c,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_in_group1) ).
cnf(b_maps_to_g,hypothesis,
an_isomorphism(b) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_g) ).
cnf(h_times_h_is_g,hypothesis,
product(g2,h,h,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_h_is_g) ).
cnf(a_times_c_is_c,hypothesis,
product(g1,a,c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_c) ).
cnf(a_times_b_is_b,hypothesis,
product(g1,a,b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_b) ).
cnf(f_times_h_is_h,hypothesis,
product(g2,f,h,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_h_is_h) ).
cnf(b_in_group1,hypothesis,
group_member(b,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_group1) ).
cnf(c_times_a_is_c,hypothesis,
product(g1,c,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_a_is_c) ).
cnf(f_times_g_is_g,hypothesis,
product(g2,f,g,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_g_is_g) ).
cnf(h_times_f_is_h,hypothesis,
product(g2,h,f,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_f_is_h) ).
cnf(c_times_b_is_a,hypothesis,
product(g1,c,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_b_is_a) ).
cnf(b_times_a_is_b,hypothesis,
product(g1,b,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_is_b) ).
cnf(h_times_g_is_f,hypothesis,
product(g2,h,g,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_g_is_f) ).
cnf(b_times_c_is_a,hypothesis,
product(g1,b,c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_c_is_a) ).
cnf(g_times_f_is_g,hypothesis,
product(g2,g,f,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_f_is_g) ).
cnf(b_times_b_is_c,hypothesis,
product(g1,b,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_c) ).
cnf(g_times_h_is_f,hypothesis,
product(g2,g,h,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_h_is_f) ).
cnf(g_times_g_is_h,hypothesis,
product(g2,g,g,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_g_is_h) ).
cnf(c_0_32,hypothesis,
( X1 = a
| X1 = b
| X1 = c
| ~ group_member(X1,g1) ),
all_of_group1 ).
cnf(c_0_33,hypothesis,
group_member(d3,g1),
d3_in_group1 ).
cnf(c_0_34,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
prove_product_holds_in_group2 ).
cnf(c_0_35,hypothesis,
( d3 = c
| d3 = b
| d3 = a ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,hypothesis,
an_isomorphism(a) = f,
a_maps_to_f ).
cnf(c_0_37,hypothesis,
group_member(d2,g1),
d2_in_group1 ).
cnf(c_0_38,negated_conjecture,
( d3 = b
| d3 = c
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),f) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,hypothesis,
( d2 = c
| d2 = b
| d2 = a ),
inference(spm,[status(thm)],[c_0_32,c_0_37]) ).
cnf(c_0_40,hypothesis,
group_member(d1,g1),
d1_in_group1 ).
cnf(c_0_41,hypothesis,
product(g1,d1,d2,d3),
d1_times_d2_is_d3 ).
cnf(c_0_42,hypothesis,
( d2 = b
| d2 = c
| d3 = c
| d3 = b
| ~ product(g2,an_isomorphism(d1),f,f) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_36]) ).
cnf(c_0_43,hypothesis,
( d1 = c
| d1 = b
| d1 = a ),
inference(spm,[status(thm)],[c_0_32,c_0_40]) ).
cnf(c_0_44,hypothesis,
product(g2,f,f,f),
f_times_f_is_f ).
cnf(c_0_45,axiom,
( X5 = X4
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X2,X3,X5) ),
total_function2 ).
cnf(c_0_46,axiom,
( product(X2,X1,X3,multiply(X2,X1,X3))
| ~ group_member(X1,X2)
| ~ group_member(X3,X2) ),
total_function1_1 ).
cnf(c_0_47,hypothesis,
( d2 = b
| d2 = c
| product(g1,d1,a,d3) ),
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_48,hypothesis,
( d1 = b
| d1 = c
| d3 = b
| d3 = c
| d2 = c
| d2 = b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_36]),c_0_44])]) ).
cnf(c_0_49,hypothesis,
product(g1,a,a,a),
a_times_a_is_a ).
cnf(c_0_50,plain,
( X1 = multiply(X2,X3,X4)
| ~ product(X2,X3,X4,X1)
| ~ group_member(X4,X2)
| ~ group_member(X3,X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,hypothesis,
( d3 = b
| d1 = c
| d1 = b
| d2 = c
| d2 = b
| product(g1,d1,a,c) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,hypothesis,
group_member(a,g1),
a_in_group1 ).
cnf(c_0_53,hypothesis,
( X1 = a
| ~ product(g1,a,a,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_49]) ).
cnf(c_0_54,hypothesis,
( X1 = d3
| ~ product(g1,d1,d2,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_41]) ).
cnf(c_0_55,hypothesis,
product(g1,c,c,b),
c_times_c_is_b ).
cnf(c_0_56,hypothesis,
( multiply(g1,d1,a) = c
| d2 = b
| d2 = c
| d1 = b
| d1 = c
| d3 = b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_40])]) ).
cnf(c_0_57,hypothesis,
multiply(g1,a,a) = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_46]),c_0_52])]) ).
cnf(c_0_58,hypothesis,
( d1 = b
| d1 = c
| a != b ),
inference(ef,[status(thm)],[c_0_43]) ).
cnf(c_0_59,hypothesis,
( d1 = b
| d1 = c
| a != c ),
inference(ef,[status(thm)],[c_0_43]) ).
cnf(c_0_60,hypothesis,
( d2 = b
| d2 = c
| a != c ),
inference(ef,[status(thm)],[c_0_39]) ).
cnf(c_0_61,hypothesis,
an_isomorphism(c) = h,
c_maps_to_h ).
cnf(c_0_62,hypothesis,
multiply(g1,d1,d2) = d3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_46]),c_0_37]),c_0_40])]) ).
cnf(c_0_63,hypothesis,
( X1 = b
| ~ product(g1,c,c,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_55]) ).
cnf(c_0_64,hypothesis,
group_member(c,g1),
c_in_group1 ).
cnf(c_0_65,hypothesis,
( d1 = b
| d1 = c
| d3 = b
| d2 = c
| d2 = b ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_43]),c_0_57])]),c_0_58]),c_0_59]) ).
cnf(c_0_66,negated_conjecture,
( d2 = b
| a != c
| ~ product(g2,an_isomorphism(d1),h,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_60]),c_0_61]) ).
cnf(c_0_67,hypothesis,
( multiply(g1,d1,c) = d3
| d2 = b
| a != c ),
inference(spm,[status(thm)],[c_0_62,c_0_60]) ).
cnf(c_0_68,hypothesis,
multiply(g1,c,c) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_46]),c_0_64])]) ).
cnf(c_0_69,hypothesis,
( d1 = c
| d1 = b
| d2 = c
| d2 = b
| product(g1,d1,a,b) ),
inference(spm,[status(thm)],[c_0_47,c_0_65]) ).
cnf(c_0_70,hypothesis,
( d1 = b
| d2 = b
| a != c
| ~ product(g2,h,h,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_59]),c_0_61]) ).
cnf(c_0_71,hypothesis,
( d1 = b
| d2 = b
| d3 = b
| a != c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_59]),c_0_68]) ).
cnf(c_0_72,hypothesis,
an_isomorphism(b) = g,
b_maps_to_g ).
cnf(c_0_73,hypothesis,
product(g2,h,h,g),
h_times_h_is_g ).
cnf(c_0_74,hypothesis,
product(g1,a,c,c),
a_times_c_is_c ).
cnf(c_0_75,hypothesis,
( multiply(g1,d1,a) = b
| d2 = b
| d2 = c
| d1 = b
| d1 = c ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_69]),c_0_52]),c_0_40])]) ).
cnf(c_0_76,hypothesis,
( d2 = b
| d1 = b
| a != c ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73])]) ).
cnf(c_0_77,hypothesis,
( X1 = c
| ~ product(g1,a,c,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_74]) ).
cnf(c_0_78,negated_conjecture,
( d1 = b
| d1 = c
| ~ product(g2,f,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_43]),c_0_36]) ).
cnf(c_0_79,hypothesis,
( d1 = b
| d1 = c
| d2 = c
| d2 = b ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_43]),c_0_57])]),c_0_76]),c_0_58]) ).
cnf(c_0_80,hypothesis,
( multiply(g1,a,d2) = d3
| d1 = b
| d1 = c ),
inference(spm,[status(thm)],[c_0_62,c_0_43]) ).
cnf(c_0_81,hypothesis,
multiply(g1,a,c) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_46]),c_0_64]),c_0_52])]) ).
cnf(c_0_82,hypothesis,
product(g1,a,b,b),
a_times_b_is_b ).
cnf(c_0_83,negated_conjecture,
( d2 = b
| d1 = c
| d1 = b
| ~ product(g2,f,h,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_61]) ).
cnf(c_0_84,hypothesis,
( d2 = b
| d1 = c
| d1 = b
| d3 = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_79]),c_0_81]) ).
cnf(c_0_85,hypothesis,
product(g2,f,h,h),
f_times_h_is_h ).
cnf(c_0_86,hypothesis,
( X1 = b
| ~ product(g1,a,b,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_82]) ).
cnf(c_0_87,hypothesis,
group_member(b,g1),
b_in_group1 ).
cnf(c_0_88,hypothesis,
( d1 = b
| d1 = c
| d2 = b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_61]),c_0_85])]) ).
cnf(c_0_89,hypothesis,
multiply(g1,a,b) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_46]),c_0_87]),c_0_52])]) ).
cnf(c_0_90,hypothesis,
product(g1,c,a,c),
c_times_a_is_c ).
cnf(c_0_91,negated_conjecture,
( d1 = c
| d1 = b
| ~ product(g2,f,g,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_88]),c_0_72]) ).
cnf(c_0_92,hypothesis,
( d1 = c
| d1 = b
| d3 = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_88]),c_0_89]) ).
cnf(c_0_93,hypothesis,
product(g2,f,g,g),
f_times_g_is_g ).
cnf(c_0_94,hypothesis,
( X1 = c
| ~ product(g1,c,a,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_90]) ).
cnf(c_0_95,negated_conjecture,
( d2 = b
| d2 = c
| ~ product(g2,an_isomorphism(d1),f,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_39]),c_0_36]) ).
cnf(c_0_96,hypothesis,
( d1 = b
| d1 = c ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_72]),c_0_93])]) ).
cnf(c_0_97,hypothesis,
( multiply(g1,d1,a) = d3
| d2 = b
| d2 = c ),
inference(spm,[status(thm)],[c_0_62,c_0_39]) ).
cnf(c_0_98,hypothesis,
multiply(g1,c,a) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_46]),c_0_52]),c_0_64])]) ).
cnf(c_0_99,negated_conjecture,
( d1 = b
| d2 = c
| d2 = b
| ~ product(g2,h,f,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_61]) ).
cnf(c_0_100,hypothesis,
( d1 = b
| d2 = c
| d2 = b
| d3 = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_96]),c_0_98]) ).
cnf(c_0_101,hypothesis,
product(g2,h,f,h),
h_times_f_is_h ).
cnf(c_0_102,negated_conjecture,
( d1 = b
| ~ product(g2,h,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_96]),c_0_61]) ).
cnf(c_0_103,hypothesis,
( d2 = b
| d2 = c
| d1 = b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_61]),c_0_101])]) ).
cnf(c_0_104,hypothesis,
( multiply(g1,c,d2) = d3
| d1 = b ),
inference(spm,[status(thm)],[c_0_62,c_0_96]) ).
cnf(c_0_105,hypothesis,
product(g1,c,b,a),
c_times_b_is_a ).
cnf(c_0_106,negated_conjecture,
( d2 = b
| d1 = b
| ~ product(g2,h,h,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_61]) ).
cnf(c_0_107,hypothesis,
( d2 = b
| d1 = b
| d3 = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_103]),c_0_68]) ).
cnf(c_0_108,hypothesis,
( X1 = a
| ~ product(g1,c,b,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_105]) ).
cnf(c_0_109,hypothesis,
( d1 = b
| d2 = b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_72]),c_0_73])]) ).
cnf(c_0_110,hypothesis,
multiply(g1,c,b) = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_46]),c_0_87]),c_0_64])]) ).
cnf(c_0_111,hypothesis,
product(g1,b,a,b),
b_times_a_is_b ).
cnf(c_0_112,negated_conjecture,
( d1 = b
| ~ product(g2,h,g,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_109]),c_0_72]) ).
cnf(c_0_113,hypothesis,
( d1 = b
| d3 = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_109]),c_0_110]) ).
cnf(c_0_114,hypothesis,
product(g2,h,g,f),
h_times_g_is_f ).
cnf(c_0_115,hypothesis,
( X1 = b
| ~ product(g1,b,a,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_111]) ).
cnf(c_0_116,hypothesis,
d1 = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_36]),c_0_114])]) ).
cnf(c_0_117,hypothesis,
multiply(g1,b,a) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_46]),c_0_52]),c_0_87])]) ).
cnf(c_0_118,hypothesis,
product(g1,b,c,a),
b_times_c_is_a ).
cnf(c_0_119,hypothesis,
( d2 = c
| d2 = b
| d3 = b ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_116]),c_0_117]) ).
cnf(c_0_120,hypothesis,
product(g2,g,f,g),
g_times_f_is_g ).
cnf(c_0_121,hypothesis,
( X1 = a
| ~ product(g1,b,c,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_118]) ).
cnf(c_0_122,negated_conjecture,
( d2 = c
| d2 = b ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_119]),c_0_116]),c_0_72]),c_0_72]),c_0_120])]) ).
cnf(c_0_123,hypothesis,
multiply(g1,b,d2) = d3,
inference(rw,[status(thm)],[c_0_62,c_0_116]) ).
cnf(c_0_124,hypothesis,
multiply(g1,b,c) = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_46]),c_0_64]),c_0_87])]) ).
cnf(c_0_125,hypothesis,
product(g1,b,b,c),
b_times_b_is_c ).
cnf(c_0_126,negated_conjecture,
( d2 = b
| ~ product(g2,g,h,an_isomorphism(d3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_122]),c_0_116]),c_0_72]),c_0_61]) ).
cnf(c_0_127,negated_conjecture,
( d2 = b
| d3 = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_122]),c_0_124]) ).
cnf(c_0_128,hypothesis,
product(g2,g,h,f),
g_times_h_is_f ).
cnf(c_0_129,hypothesis,
( X1 = c
| ~ product(g1,b,b,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_125]) ).
cnf(c_0_130,negated_conjecture,
d2 = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_36]),c_0_128])]) ).
cnf(c_0_131,hypothesis,
multiply(g1,b,b) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_46]),c_0_87])]) ).
cnf(c_0_132,hypothesis,
d3 = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_130]),c_0_131]) ).
cnf(c_0_133,hypothesis,
product(g2,g,g,h),
g_times_g_is_h ).
cnf(c_0_134,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_132]),c_0_116]),c_0_72]),c_0_130]),c_0_72]),c_0_61]),c_0_133])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP026-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.17/0.33 % Computer : n019.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon Aug 28 22:25:43 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.62 % Version : CSE_E---1.5
% 0.19/0.62 % Problem : theBenchmark.p
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark.p
% 0.19/0.62 % SZS output start Proof
% See solution above
% 0.19/0.62 % Total time : 0.062000 s
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time : 0.064000 s
%------------------------------------------------------------------------------