%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP040-4 : 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 : n027.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 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 45 ( 25 unt; 4 nHn; 32 RR)
% Number of literals : 83 ( 8 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 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 : 61 ( 0 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(product_right_cancellation,axiom,
( X4 = X2
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
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(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(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(prove_inverse_is_self_cancelling,negated_conjecture,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
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(d_in_subgroup,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_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(closure_of_inverse,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(c_0_15,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_16,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_17,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_19,axiom,
( X4 = X2
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_20,hypothesis,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_21,plain,
( product(X1,X2,X3)
| ~ product(inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_23,hypothesis,
( X1 = inverse(a)
| ~ product(b,X1,c) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
product(X1,multiply(inverse(X1),X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,hypothesis,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_26,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
closure_of_product_and_inverse ).
cnf(c_0_27,negated_conjecture,
inverse(inverse(X1)) = X1,
prove_inverse_is_self_cancelling ).
cnf(c_0_28,hypothesis,
multiply(inverse(b),c) = inverse(a),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,hypothesis,
( X1 = c
| ~ product(a,X1,d) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_30,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
property_of_O2 ).
cnf(c_0_31,hypothesis,
~ subgroup_member(d),
d_in_subgroup ).
cnf(c_0_32,hypothesis,
~ subgroup_member(a),
a_in_subgroup ).
cnf(c_0_33,negated_conjecture,
( subgroup_member(X1)
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,hypothesis,
product(inverse(b),c,inverse(a)),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_35,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
an_element_in_O2 ).
cnf(c_0_36,hypothesis,
element_in_O2(a,d) = c,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(c))
| ~ subgroup_member(inverse(b)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
closure_of_inverse ).
cnf(c_0_39,hypothesis,
subgroup_member(c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31]),c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_41,hypothesis,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_42,negated_conjecture,
( subgroup_member(X1)
| ~ subgroup_member(inverse(X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_43,negated_conjecture,
subgroup_member(inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_41])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP040-4 : 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
% 0.14/0.33 % Computer : n027.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 : Mon May 4 18:18:35 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------