%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE055+1 : TPTP v9.2.1. Released v4.0.0.
% 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 : 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 04:35:37 PM UTC 2026
% Result : Theorem 1.41s 1.77s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 30 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 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 : 45 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] :
( addition(X4,one) = one
=> addition(X4,domain(X4)) = domain(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(c_0_8,negated_conjecture,
~ ! [X4] :
( addition(X4,one) = one
=> addition(X4,domain(X4)) = domain(X4) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_9,plain,
! [X47,X48,X49] : multiplication(X47,addition(X48,X49)) = addition(multiplication(X47,X48),multiplication(X47,X49)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_10,plain,
! [X45] : multiplication(X45,one) = X45,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_11,negated_conjecture,
( addition(esk1_0,one) = one
& addition(esk1_0,domain(esk1_0)) != domain(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X35,X36] : addition(X35,X36) = addition(X36,X35),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_13,plain,
! [X50,X51,X52] : multiplication(addition(X50,X51),X52) = addition(multiplication(X50,X52),multiplication(X51,X52)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_14,plain,
! [X46] : multiplication(one,X46) = X46,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_15,plain,
! [X60] : addition(domain(X60),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
cnf(c_0_16,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
addition(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X57] : addition(X57,multiplication(domain(X57),X57)) = multiplication(domain(X57),X57),
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_21,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
addition(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19]) ).
cnf(c_0_28,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_29,negated_conjecture,
addition(X1,multiplication(X1,esk1_0)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17]) ).
cnf(c_0_30,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_28]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
addition(esk1_0,domain(esk1_0)) != domain(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_19]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE055+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n025.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 20:43:58 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.41/1.77 % Version : CSE_E---1.7
% 1.41/1.77 % Problem : theBenchmark.p
% 1.41/1.77 % SZS status Theorem for theBenchmark.p
% 1.41/1.77 % SZS output start CNFRefutation
% See solution above
% 1.41/1.77 % Total time : 1.373s
%------------------------------------------------------------------------------