%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP039-2 : TPTP v9.2.1. Released v1.0.0.
% 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 : n023.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 04:23:38 PM UTC 2026
% Result : Unsatisfiable 1.37s 1.78s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 56 ( 40 unt; 6 nHn; 33 RR)
% Number of literals : 86 ( 35 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(a_times_c_is_d,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(closure_of_multiply,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| multiply(X1,X2) != X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
cnf(b_in_O2,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_O2) ).
cnf(prove_d_in_O2,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_in_O2) ).
cnf(closure_of_inverse,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_inverse) ).
cnf(property_of_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| multiply(X1,element_in_O2(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(c_0_13,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_14,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_15,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_16,negated_conjecture,
multiply(a,c) = d,
a_times_c_is_d ).
cnf(c_0_17,negated_conjecture,
multiply(b,inverse(a)) = c,
b_times_a_inverse_is_c ).
cnf(c_0_18,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_20,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse ).
cnf(c_0_21,negated_conjecture,
multiply(a,multiply(c,X1)) = multiply(d,X1),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
multiply(b,multiply(inverse(a),X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_23,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_19]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_25,negated_conjecture,
multiply(inverse(a),d) = c,
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_26,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| multiply(X1,X2) != X3 ),
closure_of_multiply ).
cnf(c_0_27,negated_conjecture,
multiply(d,inverse(c)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_19]) ).
cnf(c_0_28,negated_conjecture,
multiply(c,a) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_19]),c_0_23]) ).
cnf(c_0_29,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24]),c_0_19]) ).
cnf(c_0_30,negated_conjecture,
multiply(c,d) = multiply(b,c),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_31,plain,
( subgroup_member(multiply(X1,X2))
| ~ subgroup_member(X2)
| ~ subgroup_member(X1) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
subgroup_member(b),
b_in_O2 ).
cnf(c_0_33,negated_conjecture,
~ subgroup_member(d),
prove_d_in_O2 ).
cnf(c_0_34,negated_conjecture,
multiply(inverse(d),a) = inverse(c),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
multiply(c,multiply(a,inverse(b))) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
multiply(d,inverse(multiply(b,c))) = inverse(c),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_17]),c_0_32])]) ).
cnf(c_0_38,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
closure_of_inverse ).
cnf(c_0_39,negated_conjecture,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_16]),c_0_33]) ).
cnf(c_0_40,plain,
( subgroup_member(multiply(X1,multiply(X2,X3)))
| ~ subgroup_member(multiply(X1,X2))
| ~ subgroup_member(X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_41,negated_conjecture,
multiply(inverse(d),multiply(a,X1)) = multiply(inverse(c),X1),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
multiply(a,inverse(b)) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_35]),c_0_19]) ).
cnf(c_0_43,negated_conjecture,
multiply(inverse(d),inverse(c)) = inverse(multiply(b,c)),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_44,plain,
( subgroup_member(X1)
| ~ subgroup_member(multiply(X2,X1))
| ~ subgroup_member(inverse(X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_18]) ).
cnf(c_0_45,negated_conjecture,
~ subgroup_member(a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_46,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| multiply(X1,element_in_O2(X1,X2)) = X2 ),
property_of_O2 ).
cnf(c_0_47,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
an_element_in_O2 ).
cnf(c_0_48,plain,
( subgroup_member(X1)
| ~ subgroup_member(multiply(X1,X2))
| ~ subgroup_member(inverse(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_20]),c_0_19]) ).
cnf(c_0_49,negated_conjecture,
multiply(inverse(c),inverse(b)) = inverse(multiply(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_50,negated_conjecture,
~ subgroup_member(inverse(c)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_28]),c_0_32])]),c_0_45]) ).
cnf(c_0_51,plain,
( subgroup_member(multiply(X1,X2))
| subgroup_member(X3)
| subgroup_member(X2)
| ~ subgroup_member(multiply(X1,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_46]),c_0_47]) ).
cnf(c_0_52,negated_conjecture,
~ subgroup_member(inverse(multiply(b,c))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_23]),c_0_32])]),c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( subgroup_member(multiply(c,X1))
| subgroup_member(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_28]),c_0_32])]),c_0_45]) ).
cnf(c_0_54,negated_conjecture,
~ subgroup_member(multiply(b,c)),
inference(spm,[status(thm)],[c_0_52,c_0_38]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_30]),c_0_54]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP039-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n023.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 18:19:23 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.37/1.78 % Version : CSE_E---1.7
% 1.37/1.78 % Problem : theBenchmark.p
% 1.37/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 1.37/1.78 % SZS output start CNFRefutation
% See solution above
% 1.37/1.78 % Total time : 1.371s
%------------------------------------------------------------------------------