%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO011-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n025.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 04:11:06 PM UTC 2026
% Result : Unsatisfiable 0.28s 1.60s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 31
% Syntax : Number of clauses : 77 ( 63 unt; 0 nHn; 14 RR)
% Number of literals : 93 ( 92 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity3,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
cnf(distributivity1,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(distributivity4,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
cnf(distributivity2,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(multiplicative_inverse2,axiom,
multiply(inverse(X1),X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse2) ).
cnf(additive_inverse2,axiom,
add(inverse(X1),X1) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse2) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(additive_id2,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(prove_inverse_of_1_is_0,negated_conjecture,
inverse(additive_identity) != multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_1_is_0) ).
cnf(i_0_15,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distributivity3,
[final] ).
cnf(i_0_16,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
distributivity1,
[final] ).
cnf(i_0_17,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity4,
[final] ).
cnf(i_0_18,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity2,
[final] ).
cnf(i_0_19,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply,
[final] ).
cnf(i_0_20,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add,
[final] ).
cnf(i_0_21,axiom,
multiply(inverse(X1),X1) = additive_identity,
multiplicative_inverse2,
[final] ).
cnf(i_0_22,axiom,
add(inverse(X1),X1) = multiplicative_identity,
additive_inverse2,
[final] ).
cnf(i_0_23,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1,
[final] ).
cnf(i_0_24,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1,
[final] ).
cnf(i_0_25,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2,
[final] ).
cnf(i_0_26,axiom,
add(additive_identity,X1) = X1,
additive_id2,
[final] ).
cnf(i_0_27,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1,
[final] ).
cnf(i_0_28,axiom,
add(X1,additive_identity) = X1,
additive_id1,
[final] ).
cnf(i_0_29,negated_conjecture,
inverse(additive_identity) != multiplicative_identity,
prove_inverse_of_1_is_0,
[final] ).
cnf(i_0_30,axiom,
X1 = X1 ).
cnf(i_0_31,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_32,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_33,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_34,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| add(X1,X3) = add(X2,X3) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| add(X3,X1) = add(X3,X2) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_30_001,axiom,
X1 = X1 ).
cnf(i_0_31_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_32_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_33_004,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_34_005,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_35_006,axiom,
( X1 != X2
| add(X1,X3) = add(X2,X3) ) ).
cnf(i_0_36_007,axiom,
( X1 != X2
| add(X3,X1) = add(X3,X2) ) ).
cnf(i_0_37_008,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_38,plain,
X1 = multiply(multiplicative_identity,X1),
inference(scs_inference,[],[i_0_25,i_0_31]) ).
cnf(i_0_39,plain,
inverse(additive_identity) != multiply(multiplicative_identity,multiplicative_identity),
inference(scs_inference,[],[i_0_29,i_0_25,i_0_31,i_0_32]) ).
cnf(i_0_40,plain,
multiply(multiplicative_identity,X1) = X1,
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_41,plain,
X1 = add(additive_identity,X1),
inference(scs_inference,[],[i_0_26,i_0_31]) ).
cnf(i_0_42,plain,
inverse(additive_identity) != add(additive_identity,multiplicative_identity),
inference(scs_inference,[],[i_0_29,i_0_26,i_0_31,i_0_32]) ).
cnf(i_0_43,plain,
add(additive_identity,X1) = X1,
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_44,plain,
X1 = multiply(X1,multiplicative_identity),
inference(scs_inference,[],[i_0_27,i_0_31]) ).
cnf(i_0_45,plain,
inverse(additive_identity) != add(multiplicative_identity,additive_identity),
inference(scs_inference,[],[i_0_42,i_0_20,i_0_27,i_0_31,i_0_32]) ).
cnf(i_0_46,plain,
add(X1,X2) = add(X2,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_47,plain,
X1 = add(X1,additive_identity),
inference(scs_inference,[],[i_0_28,i_0_31]) ).
cnf(i_0_48,plain,
add(X1,X2) = add(multiply(X1,multiplicative_identity),multiply(X2,multiplicative_identity)),
inference(scs_inference,[],[i_0_44,i_0_28,i_0_15,i_0_31,i_0_32]) ).
cnf(i_0_49,plain,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_50,plain,
X1 = multiply(X1,multiplicative_identity),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_51,plain,
add(multiply(X1,multiplicative_identity),multiply(X2,multiplicative_identity)) = add(X1,X2),
inference(scs_inference,[],[i_0_48,i_0_31]) ).
cnf(i_0_52,plain,
X1 = add(multiply(additive_identity,multiplicative_identity),multiply(X1,multiplicative_identity)),
inference(scs_inference,[],[i_0_41,i_0_48,i_0_31,i_0_32]) ).
cnf(i_0_53,plain,
add(X1,X2) = add(multiply(X1,multiplicative_identity),multiply(X2,multiplicative_identity)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_54,plain,
add(multiply(additive_identity,multiplicative_identity),multiply(X1,multiplicative_identity)) = X1,
inference(scs_inference,[],[i_0_52,i_0_31]) ).
cnf(i_0_55,plain,
inverse(additive_identity) != add(multiply(multiplicative_identity,multiplicative_identity),multiply(additive_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_51,i_0_52,i_0_45,i_0_31,i_0_32]) ).
cnf(i_0_56,plain,
add(multiply(X1,multiplicative_identity),multiply(X2,multiplicative_identity)) = add(X1,X2),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_57,plain,
multiply(add(X1,X2),add(X3,X2)) = add(multiply(X1,X3),X2),
inference(scs_inference,[],[i_0_16,i_0_31]) ).
cnf(i_0_58,plain,
inverse(additive_identity) != add(multiply(additive_identity,multiplicative_identity),multiply(multiplicative_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_29,i_0_54,i_0_16,i_0_31,i_0_32]) ).
cnf(i_0_59,plain,
add(multiply(additive_identity,multiplicative_identity),multiply(X1,multiplicative_identity)) = X1,
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_60,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(scs_inference,[],[i_0_17,i_0_31]) ).
cnf(i_0_61,plain,
add(X1,X2) = add(multiply(multiplicative_identity,X1),multiply(multiplicative_identity,X2)),
inference(scs_inference,[],[i_0_38,i_0_17,i_0_31,i_0_32]) ).
cnf(i_0_62,plain,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_63,plain,
X1 = multiply(multiplicative_identity,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_64,plain,
add(multiply(multiplicative_identity,X1),multiply(multiplicative_identity,X2)) = add(X1,X2),
inference(scs_inference,[],[i_0_61,i_0_31]) ).
cnf(i_0_65,plain,
multiply(add(X1,X2),add(X3,X2)) = add(multiply(multiplicative_identity,multiply(X1,X3)),multiply(multiplicative_identity,X2)),
inference(scs_inference,[],[i_0_57,i_0_61,i_0_31,i_0_32]) ).
cnf(i_0_66,plain,
add(X1,X2) = add(multiply(multiplicative_identity,X1),multiply(multiplicative_identity,X2)),
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_67,plain,
add(multiply(multiplicative_identity,multiply(X1,X2)),multiply(multiplicative_identity,X3)) = multiply(add(X1,X3),add(X2,X3)),
inference(scs_inference,[],[i_0_65,i_0_31]) ).
cnf(i_0_68,plain,
$false,
inference(scs_inference,[],[i_0_29,i_0_47,i_0_65,i_0_22,i_0_31,i_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : BOO011-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.10 % 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
% 0.13/0.31 % Computer : n025.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue May 5 10:44:43 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 0.28/1.60 % Version : CSE_E---1.7
% 0.28/1.60 % Problem : theBenchmark.p
% 0.28/1.60 % SZS status Unsatisfiable for theBenchmark.p
% 0.28/1.60 % SZS output start CNFRefutation
% See solution above
% 0.28/1.65 % Total time : 1.271s
%------------------------------------------------------------------------------