%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP012-1 : 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 : n001.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 04:23:33 PM UTC 2026
% Result : Unsatisfiable 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 18 unt; 0 nHn; 21 RR)
% Number of literals : 48 ( 8 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(inverse_b_multiply_inverse_a_is_d,hypothesis,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
cnf(a_multiply_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
cnf(prove_c_multiply_d_is_identity,negated_conjecture,
~ product(c,d,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_multiply_d_is_identity) ).
cnf(c_0_8,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_9,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_10,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_11,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_12,plain,
( X1 = X2
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_14,plain,
( product(X1,inverse(X2),X3)
| ~ product(X4,identity,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,hypothesis,
product(inverse(b),inverse(a),d),
inverse_b_multiply_inverse_a_is_d ).
cnf(c_0_17,plain,
( product(X1,inverse(X2),X3)
| ~ product(X3,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15]) ).
cnf(c_0_18,hypothesis,
product(a,b,c),
a_multiply_b_is_c ).
cnf(c_0_19,hypothesis,
( product(X1,inverse(a),X2)
| ~ product(X3,inverse(b),X1)
| ~ product(X3,d,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_20,hypothesis,
product(c,inverse(b),a),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,hypothesis,
( product(a,inverse(a),X1)
| ~ product(c,d,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
( X1 = identity
| ~ product(X2,inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_23,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_24,hypothesis,
product(a,inverse(a),multiply(c,d)),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_25,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_26,hypothesis,
multiply(c,d) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,negated_conjecture,
~ product(c,d,identity),
prove_c_multiply_d_is_identity ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP012-1 : 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
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:18:18 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------