%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE119+1 : TPTP v9.2.1. Released v4.0.0.
% 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 : n029.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 04:35:45 PM UTC 2026
% Result : Theorem 1.26s 1.70s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 1 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] : addition(backward_diamond(zero,domain(X4)),domain(X5)) = domain(X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(c_0_10,negated_conjecture,
~ ! [X4,X5] : addition(backward_diamond(zero,domain(X4)),domain(X5)) = domain(X5),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_11,plain,
! [X88,X89] : backward_diamond(X88,X89) = codomain(multiplication(codomain(X89),X88)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_12,plain,
! [X82] : codomain(X82) = coantidomain(coantidomain(X82)),
inference(variable_rename,[status(thm)],[codomain4]) ).
fof(c_0_13,negated_conjecture,
addition(backward_diamond(zero,domain(esk1_0)),domain(esk2_0)) != domain(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_14,plain,
! [X77] : domain(X77) = antidomain(antidomain(X77)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_15,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X81] : addition(coantidomain(coantidomain(X81)),coantidomain(X81)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_18,plain,
! [X51,X52] : addition(X51,X52) = addition(X52,X51),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_19,plain,
! [X78] : multiplication(X78,coantidomain(X78)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_20,plain,
! [X62] : multiplication(one,X62) = X62,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_21,plain,
! [X56] : addition(X56,zero) = X56,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_22,negated_conjecture,
addition(backward_diamond(zero,domain(esk1_0)),domain(esk2_0)) != domain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
fof(c_0_25,plain,
! [X69] : multiplication(X69,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_26,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),zero))),antidomain(antidomain(esk2_0))) != antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_24]) ).
cnf(c_0_32,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_36,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(zero))) != antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_27]) ).
cnf(c_0_37,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_34]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE119+1 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.13/0.31 % Computer : n029.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 : Mon May 4 20:30:44 EDT 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.32 % start to proof: theBenchmark
% 1.26/1.70 % Version : CSE_E---1.7
% 1.26/1.70 % Problem : theBenchmark.p
% 1.26/1.70 % SZS status Theorem for theBenchmark.p
% 1.26/1.70 % SZS output start CNFRefutation
% See solution above
% 1.26/1.70 % Total time : 1.371s
%------------------------------------------------------------------------------