%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP048-10 : TPTP v9.2.1. Released v7.5.0.
% 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 : n003.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 04:23:40 PM UTC 2026
% Result : Unsatisfiable 21.84s 13.02s
% Output : CNFRefutation 21.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 12 RR)
% Number of literals : 44 ( 43 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 80 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
cnf(product_substitution3,axiom,
ifeq(equalish(X1,X2),true,ifeq(product(X3,X4,X1),true,product(X3,X4,X2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
cnf(left_identity,axiom,
product(identity,X1,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(total_function2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,equalish(X4,X3),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
cnf(a_equals_b,hypothesis,
equalish(a,b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
cnf(prove_inverse_substitution,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_substitution) ).
cnf(c_0_9,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
associativity2 ).
cnf(c_0_10,axiom,
product(inverse(X1),X1,identity) = true,
left_inverse ).
cnf(c_0_11,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_12,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(inverse(X1),X3,X4),true,product(identity,X2,X4),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,axiom,
product(X1,X2,multiply(X1,X2)) = true,
total_function1 ).
cnf(c_0_14,axiom,
ifeq(equalish(X1,X2),true,ifeq(product(X3,X4,X1),true,product(X3,X4,X2),true),true) = true,
product_substitution3 ).
cnf(c_0_15,axiom,
product(identity,X1,X1) = true,
left_identity ).
cnf(c_0_16,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,equalish(X4,X3),true),true) = true,
total_function2 ).
cnf(c_0_17,plain,
ifeq(product(X1,X2,X3),true,product(identity,X2,multiply(inverse(X1),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]) ).
cnf(c_0_18,plain,
ifeq(equalish(X1,X2),true,product(identity,X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_11]) ).
cnf(c_0_19,hypothesis,
equalish(a,b) = true,
a_equals_b ).
cnf(c_0_20,plain,
ifeq(product(identity,X1,X2),true,equalish(X2,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_11]) ).
cnf(c_0_21,plain,
product(identity,X1,multiply(inverse(inverse(X1)),identity)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10]),c_0_11]) ).
cnf(c_0_22,hypothesis,
product(identity,a,b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_11]) ).
cnf(c_0_23,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(inverse(X3),X1,X4),true,product(X4,X2,identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_24,plain,
ifeq(equalish(multiply(X1,X2),X3),true,product(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_11]) ).
cnf(c_0_25,plain,
equalish(multiply(inverse(inverse(X1)),identity),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_11]) ).
cnf(c_0_26,hypothesis,
ifeq(product(identity,a,X1),true,equalish(X1,b),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_11]) ).
cnf(c_0_27,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X1,X5),true,product(X5,X2,multiply(X4,X3)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_13]),c_0_11]) ).
cnf(c_0_28,plain,
ifeq(product(inverse(X1),identity,X2),true,product(X2,X1,identity),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_15]),c_0_11]) ).
cnf(c_0_29,plain,
product(inverse(inverse(X1)),identity,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11]) ).
cnf(c_0_30,hypothesis,
equalish(multiply(inverse(inverse(a)),identity),b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_11]) ).
cnf(c_0_31,plain,
ifeq(product(X1,inverse(X2),X3),true,product(X3,X2,multiply(X1,identity)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_10]),c_0_11]) ).
cnf(c_0_32,plain,
product(X1,inverse(X1),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_11]) ).
cnf(c_0_33,hypothesis,
product(inverse(inverse(a)),identity,b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_11]) ).
cnf(c_0_34,plain,
product(identity,X1,multiply(X1,identity)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_11]) ).
cnf(c_0_35,hypothesis,
product(b,inverse(a),identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_33]),c_0_11]) ).
cnf(c_0_36,plain,
equalish(multiply(X1,identity),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_34]),c_0_11]) ).
cnf(c_0_37,hypothesis,
product(identity,inverse(a),multiply(inverse(b),identity)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_35]),c_0_11]) ).
cnf(c_0_38,plain,
product(X1,identity,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_36]),c_0_11]) ).
cnf(c_0_39,hypothesis,
equalish(multiply(inverse(b),identity),inverse(a)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_37]),c_0_11]) ).
cnf(c_0_40,plain,
ifeq(product(X1,identity,X2),true,equalish(X2,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_38]),c_0_11]) ).
cnf(c_0_41,hypothesis,
product(inverse(b),identity,inverse(a)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_11]) ).
cnf(c_0_42,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
prove_inverse_substitution ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_11]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP048-10 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:20:26 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 21.84/13.02 % Version : CSE_E---1.7
% 21.84/13.02 % Problem : theBenchmark.p
% 21.84/13.02 % SZS status Unsatisfiable for theBenchmark.p
% 21.84/13.02 % SZS output start CNFRefutation
% See solution above
% 21.96/13.08 % Total time : 10.378s
%------------------------------------------------------------------------------