%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP040-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n031.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 04:23:39 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 65 ( 36 unt; 7 nHn; 45 RR)
% Number of literals : 122 ( 18 equ; 49 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 99 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(a_times_c_is_d,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(prove_inverse_is_self_cancelling,negated_conjecture,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(property_of_O2,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
cnf(b_times_a_inverse_is_c,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(closure_of_product_and_inverse,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(d_in_subgroup,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_in_subgroup) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(a_in_subgroup,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_in_subgroup) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(c_0_17,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_18,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_19,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_21,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_22,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_23,plain,
( product(X1,X2,X3)
| ~ product(inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
product(X1,multiply(inverse(X1),X2),X2),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_26,hypothesis,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_27,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
inverse(inverse(X1)) = X1,
prove_inverse_is_self_cancelling ).
cnf(c_0_29,hypothesis,
( X1 = d
| ~ product(a,c,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,hypothesis,
multiply(a,c) = d,
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_32,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_33,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
property_of_O2 ).
cnf(c_0_34,hypothesis,
multiply(inverse(a),d) = c,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,hypothesis,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_36,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
closure_of_product_and_inverse ).
cnf(c_0_37,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_38,plain,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X3,element_in_O2(X1,X2),X4)
| ~ product(X5,X2,X4)
| ~ product(X5,X1,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,hypothesis,
product(inverse(a),d,c),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_40,hypothesis,
~ subgroup_member(d),
d_in_subgroup ).
cnf(c_0_41,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_42,hypothesis,
( X1 = c
| ~ product(b,inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_43,plain,
( subgroup_member(identity)
| ~ subgroup_member(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_28])]) ).
cnf(c_0_44,hypothesis,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_45,plain,
( X1 = X2
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_46,hypothesis,
( subgroup_member(X1)
| product(X2,element_in_O2(X1,d),c)
| ~ product(inverse(a),X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_47,plain,
( X1 = X2
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( subgroup_member(X1)
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_49,hypothesis,
multiply(b,inverse(a)) = c,
inference(spm,[status(thm)],[c_0_42,c_0_22]) ).
cnf(c_0_50,hypothesis,
subgroup_member(identity),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,hypothesis,
( element_in_O2(X1,d) = c
| subgroup_member(X1)
| ~ product(inverse(a),X1,identity) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_22]) ).
cnf(c_0_53,hypothesis,
~ subgroup_member(a),
a_in_subgroup ).
cnf(c_0_54,negated_conjecture,
( subgroup_member(multiply(X1,X2))
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_22]) ).
cnf(c_0_55,hypothesis,
multiply(inverse(b),c) = inverse(a),
inference(spm,[status(thm)],[c_0_30,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( subgroup_member(X1)
| ~ subgroup_member(inverse(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_18]),c_0_50])]) ).
cnf(c_0_57,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
an_element_in_O2 ).
cnf(c_0_58,hypothesis,
element_in_O2(a,d) = c,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_25]),c_0_28]),c_0_52]),c_0_28]),c_0_52]),c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(c))
| ~ subgroup_member(inverse(b)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_28]) ).
cnf(c_0_61,hypothesis,
subgroup_member(c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_40]),c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_63,negated_conjecture,
subgroup_member(inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_60]),c_0_44])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_63]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP040-3 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:20:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------