%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO014-2 : 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 : n023.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 04:11:08 PM UTC 2026
% Result : Unsatisfiable 1.64s 1.86s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 29 RR)
% Number of literals : 81 ( 80 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 89 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(distributivity4,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
cnf(additive_id2,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(a_inverse_times_b_inverse_is_d,hypothesis,
multiply(inverse(a),inverse(b)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse_is_d) ).
cnf(a_plus_b_is_c,hypothesis,
add(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_plus_b_is_c) ).
cnf(prove_c_inverse_is_d,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c_0_13,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity2 ).
cnf(c_0_14,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_15,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_16,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2 ).
cnf(c_0_18,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity4 ).
cnf(c_0_19,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
cnf(c_0_20,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_21,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_22,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_23,axiom,
add(additive_identity,X1) = X1,
additive_id2 ).
cnf(c_0_24,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_19]),c_0_15]),c_0_20]) ).
cnf(c_0_25,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X2,additive_identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_21]),c_0_22]) ).
cnf(c_0_26,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X2,additive_identity)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_28,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_29,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_17]) ).
cnf(c_0_30,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_31,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_21]) ).
cnf(c_0_32,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21]) ).
cnf(c_0_33,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_28]),c_0_21]) ).
cnf(c_0_34,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_23]) ).
cnf(c_0_35,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]) ).
cnf(c_0_36,plain,
add(X1,add(inverse(X1),X2)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_33]),c_0_14]) ).
cnf(c_0_37,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_14]),c_0_15]),c_0_35]) ).
cnf(c_0_38,hypothesis,
multiply(inverse(a),inverse(b)) = d,
a_inverse_times_b_inverse_is_d ).
cnf(c_0_39,plain,
add(inverse(X1),add(X1,X2)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,hypothesis,
add(d,inverse(a)) = inverse(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_38]),c_0_20]) ).
cnf(c_0_41,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_42,hypothesis,
add(inverse(a),inverse(d)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20]) ).
cnf(c_0_43,hypothesis,
add(d,inverse(b)) = inverse(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_20]) ).
cnf(c_0_44,hypothesis,
add(a,b) = c,
a_plus_b_is_c ).
cnf(c_0_45,hypothesis,
multiply(a,inverse(d)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_42]),c_0_15]) ).
cnf(c_0_46,hypothesis,
add(inverse(b),inverse(d)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_43]),c_0_20]) ).
cnf(c_0_47,hypothesis,
add(b,multiply(additive_identity,a)) = multiply(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_44]),c_0_22]) ).
cnf(c_0_48,hypothesis,
multiply(c,add(a,X1)) = add(a,multiply(X1,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_44]),c_0_22]) ).
cnf(c_0_49,hypothesis,
add(a,inverse(d)) = inverse(d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_45]),c_0_20]) ).
cnf(c_0_50,hypothesis,
multiply(b,inverse(d)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_46]),c_0_15]) ).
cnf(c_0_51,plain,
add(X1,add(X2,inverse(X1))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_14]) ).
cnf(c_0_52,plain,
add(X1,multiply(multiply(X2,X1),X3)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_41]),c_0_25]),c_0_28]),c_0_21]) ).
cnf(c_0_53,hypothesis,
multiply(b,c) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_26]),c_0_21]) ).
cnf(c_0_54,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_21]) ).
cnf(c_0_55,hypothesis,
add(a,inverse(b)) = add(a,d),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_56,hypothesis,
multiply(c,inverse(d)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_22]),c_0_50]),c_0_44]) ).
cnf(c_0_57,plain,
add(inverse(X1),add(X2,X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_51,c_0_37]) ).
cnf(c_0_58,hypothesis,
add(c,multiply(b,X1)) = c,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
multiply(inverse(X1),add(X2,X1)) = multiply(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_54,c_0_37]) ).
cnf(c_0_60,hypothesis,
add(b,add(a,d)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_51,c_0_55]) ).
cnf(c_0_61,hypothesis,
add(c,inverse(d)) = inverse(d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_56]),c_0_20]) ).
cnf(c_0_62,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_30]),c_0_21]) ).
cnf(c_0_63,hypothesis,
add(c,inverse(multiply(b,X1))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_20]) ).
cnf(c_0_64,hypothesis,
multiply(b,inverse(add(a,d))) = inverse(add(a,d)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_15]),c_0_22]) ).
cnf(c_0_65,hypothesis,
add(inverse(c),inverse(d)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_39,c_0_61]) ).
cnf(c_0_66,plain,
multiply(X1,multiply(X2,inverse(X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_30]) ).
cnf(c_0_67,hypothesis,
add(a,multiply(a,b)) = multiply(a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_62]),c_0_22]) ).
cnf(c_0_68,plain,
add(X1,add(X2,X1)) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_31]),c_0_20]) ).
cnf(c_0_69,plain,
multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_70,plain,
multiply(inverse(X1),add(X1,X2)) = multiply(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_71,hypothesis,
add(c,add(a,d)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_37]) ).
cnf(c_0_72,hypothesis,
multiply(d,inverse(c)) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_65]),c_0_15]) ).
cnf(c_0_73,plain,
multiply(inverse(X1),multiply(X2,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_66,c_0_37]) ).
cnf(c_0_74,hypothesis,
multiply(a,c) = a,
inference(rw,[status(thm)],[c_0_67,c_0_24]) ).
cnf(c_0_75,plain,
add(X1,multiply(X2,add(X3,X1))) = add(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_68]),c_0_69]) ).
cnf(c_0_76,hypothesis,
multiply(inverse(c),add(a,d)) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_15]) ).
cnf(c_0_77,hypothesis,
add(d,inverse(c)) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_72]),c_0_20]) ).
cnf(c_0_78,hypothesis,
multiply(a,inverse(c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_22]) ).
cnf(c_0_79,negated_conjecture,
inverse(c) != d,
prove_c_inverse_is_d ).
cnf(c_0_80,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_22]),c_0_78]),c_0_21]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO014-2 : 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
% 0.16/0.33 % Computer : n023.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 : Tue May 5 10:45:09 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.64/1.86 % Version : CSE_E---1.7
% 1.64/1.86 % Problem : theBenchmark.p
% 1.64/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.64/1.86 % SZS output start CNFRefutation
% See solution above
% 1.64/1.86 % Total time : 1.369s
%------------------------------------------------------------------------------