%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP035-3 : 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 04:23:38 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 25 unt; 0 nHn; 28 RR)
% Number of literals : 73 ( 10 equ; 33 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
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(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
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(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
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(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
cnf(prove_c_is_in_subgroup,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).
cnf(c_0_12,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_13,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_14,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_15,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_16,plain,
( X1 = X2
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_18,plain,
( product(X1,X2,X3)
| ~ product(X4,inverse(X2),X1)
| ~ product(X4,identity,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_21,plain,
( product(X1,X2,X3)
| ~ product(X3,inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_19]) ).
cnf(c_0_22,plain,
( X1 = X2
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_23,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
closure_of_product_and_inverse ).
cnf(c_0_24,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_25,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_26,plain,
product(identity,X1,inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_27,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_28,plain,
( subgroup_member(identity)
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,hypothesis,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_30,plain,
( subgroup_member(multiply(X1,inverse(X2)))
| ~ subgroup_member(X2)
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_31,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,hypothesis,
subgroup_member(identity),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_34,plain,
( subgroup_member(multiply(X1,X2))
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_32])]) ).
cnf(c_0_36,hypothesis,
( X1 = c
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_33]) ).
cnf(c_0_37,plain,
( subgroup_member(multiply(X1,X2))
| ~ subgroup_member(X1)
| ~ subgroup_member(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_39,hypothesis,
subgroup_member(a),
a_is_in_subgroup ).
cnf(c_0_40,negated_conjecture,
~ subgroup_member(c),
prove_c_is_in_subgroup ).
cnf(c_0_41,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_29])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP035-3 : 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 18:20:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------