%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP300-1 : TPTP v9.2.1. Released v2.5.0.
% 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 : n012.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 04:25:20 PM UTC 2026
% Result : Unsatisfiable 1.13s 1.62s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of clauses : 79 ( 20 unt; 51 nHn; 69 RR)
% Number of literals : 191 ( 190 equ; 67 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c6,sk_c5) != sk_c4
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| multiply(sk_c4,sk_c6) != sk_c5
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| inverse(X2) != sk_c6
| inverse(sk_c6) != sk_c4
| multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(c_0_20,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_21,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_22,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_23,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c3,sk_c4) = sk_c5 ),
prove_this_5 ).
cnf(c_0_25,negated_conjecture,
( multiply(inverse(sk_c3),sk_c5) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| inverse(sk_c3) = sk_c4 ),
prove_this_6 ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
prove_this_23 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c6,sk_c5) != sk_c4
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| multiply(sk_c4,sk_c6) != sk_c5
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| inverse(X2) != sk_c6
| inverse(sk_c6) != sk_c4
| multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c4 ),
prove_this_25 ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c4 ),
prove_this_10 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
prove_this_7 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( multiply(inverse(sk_c3),sk_c5) = sk_c4
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c4 ),
prove_this_24 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c6,sk_c5) != sk_c4
| multiply(sk_c4,sk_c6) != sk_c5
| multiply(X1,sk_c4) != sk_c5
| multiply(X2,sk_c6) != sk_c5
| multiply(X3,sk_c6) != sk_c5
| inverse(X1) != sk_c4
| inverse(X2) != sk_c6
| inverse(X3) != sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_31]),c_0_21]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| identity = sk_c5
| multiply(sk_c4,sk_c6) != sk_c5
| multiply(X1,sk_c4) != sk_c5
| multiply(X2,sk_c6) != sk_c5
| multiply(X3,sk_c6) != sk_c5
| inverse(X1) != sk_c4
| inverse(X2) != sk_c6
| inverse(X3) != sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| identity = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_36]),c_0_21]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| identity = sk_c5
| multiply(X1,sk_c4) != sk_c5
| multiply(X2,sk_c6) != sk_c5
| multiply(X3,sk_c6) != sk_c5
| inverse(X1) != sk_c4
| inverse(X2) != sk_c6
| inverse(X3) != sk_c6 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
prove_this_11 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c4 ),
prove_this_12 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| identity = sk_c5
| multiply(X1,sk_c6) != sk_c5
| multiply(X2,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| inverse(X2) != sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
prove_this_8 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
prove_this_9 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| identity = sk_c5
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| identity = sk_c5 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c1),sk_c5) = sk_c6
| identity = sk_c5 ),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c4 ),
prove_this_22 ).
cnf(c_0_49,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c6) = sk_c5
| identity = sk_c5 ),
inference(spm,[status(thm)],[c_0_23,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c6) = sk_c4 ),
prove_this_16 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c2,sk_c6) = sk_c5 ),
prove_this_2 ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c6) = sk_c4
| identity = sk_c5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_21])]) ).
cnf(c_0_54,negated_conjecture,
multiply(sk_c4,sk_c6) = sk_c5,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_51]),c_0_38]) ).
cnf(c_0_55,negated_conjecture,
( multiply(inverse(sk_c2),sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(spm,[status(thm)],[c_0_23,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| inverse(sk_c2) = sk_c6 ),
prove_this_3 ).
cnf(c_0_57,negated_conjecture,
( multiply(inverse(sk_c1),sk_c5) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
prove_this_13 ).
cnf(c_0_59,negated_conjecture,
identity = sk_c5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_53]),c_0_54])]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
multiply(sk_c5,X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c6
| sk_c4 != sk_c6 ),
inference(ef,[status(thm)],[c_0_60]) ).
cnf(c_0_64,negated_conjecture,
multiply(inverse(sk_c4),sk_c5) = sk_c6,
inference(spm,[status(thm)],[c_0_23,c_0_54]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c4
| multiply(sk_c5,sk_c4) = sk_c6 ),
prove_this_1 ).
cnf(c_0_66,negated_conjecture,
multiply(sk_c6,sk_c5) = sk_c6,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_67,negated_conjecture,
multiply(inverse(inverse(sk_c4)),sk_c6) = sk_c5,
inference(spm,[status(thm)],[c_0_23,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
sk_c4 = sk_c6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_62]),c_0_66])]) ).
cnf(c_0_69,plain,
multiply(inverse(X1),X1) = sk_c5,
inference(rw,[status(thm)],[c_0_21,c_0_59]) ).
cnf(c_0_70,negated_conjecture,
multiply(inverse(inverse(sk_c6)),sk_c6) = sk_c5,
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
multiply(inverse(inverse(X1)),sk_c5) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( multiply(X1,sk_c6) != sk_c5
| multiply(X2,sk_c6) != sk_c5
| multiply(X3,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c6
| inverse(X1) != sk_c6
| inverse(X2) != sk_c6
| inverse(X3) != sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_54])]),c_0_66]),c_0_68]),c_0_62]),c_0_68]),c_0_68]),c_0_68]),c_0_68])]) ).
cnf(c_0_73,negated_conjecture,
inverse(sk_c6) = sk_c6,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_70]),c_0_71]) ).
cnf(c_0_74,negated_conjecture,
( multiply(X1,sk_c6) != sk_c5
| multiply(X2,sk_c6) != sk_c5
| multiply(X3,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| inverse(X2) != sk_c6
| inverse(X3) != sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
cnf(c_0_75,negated_conjecture,
multiply(sk_c6,sk_c6) = sk_c5,
inference(rw,[status(thm)],[c_0_54,c_0_68]) ).
cnf(c_0_76,negated_conjecture,
( multiply(X1,sk_c6) != sk_c5
| multiply(X2,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| inverse(X2) != sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_73])]) ).
cnf(c_0_77,negated_conjecture,
( multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_73])]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_73]),c_0_75])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP300-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 18:31:46 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.13/1.62 % Version : CSE_E---1.7
% 1.13/1.62 % Problem : theBenchmark.p
% 1.13/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/1.62 % SZS output start CNFRefutation
% See solution above
% 1.13/1.62 % Total time : 1.361s
%------------------------------------------------------------------------------