%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE090-10 : TPTP v9.2.1. Released v7.3.0.
% 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 : n020.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 04:35:41 PM UTC 2026
% Result : Unsatisfiable 4.24s 3.34s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 12 RR)
% Number of literals : 44 ( 43 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_distributivity,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
cnf(domain1,axiom,
multiplication(antidomain(X1),X1) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
cnf(additive_identity,axiom,
addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
cnf(domain3,axiom,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
cnf(additive_commutativity,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(multiplicative_right_identity,axiom,
multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(additive_associativity,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
cnf(additive_idempotence,axiom,
addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
cnf(goals,negated_conjecture,
addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(domain2,axiom,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
cnf(left_distributivity,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
cnf(multiplicative_left_identity,axiom,
multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(goals_1,negated_conjecture,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_1) ).
cnf(c_0_13,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
right_distributivity ).
cnf(c_0_14,axiom,
multiplication(antidomain(X1),X1) = zero,
domain1 ).
cnf(c_0_15,axiom,
addition(X1,zero) = X1,
additive_identity ).
cnf(c_0_16,axiom,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
domain3 ).
cnf(c_0_17,axiom,
addition(X1,X2) = addition(X2,X1),
additive_commutativity ).
cnf(c_0_18,axiom,
multiplication(X1,one) = X1,
multiplicative_right_identity ).
cnf(c_0_19,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
additive_associativity ).
cnf(c_0_20,axiom,
addition(X1,X1) = X1,
additive_idempotence ).
cnf(c_0_21,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1,
goals ).
cnf(c_0_23,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_25,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_26,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,axiom,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
domain2 ).
cnf(c_0_28,negated_conjecture,
multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14]) ).
cnf(c_0_29,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_30,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_17]) ).
cnf(c_0_31,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
left_distributivity ).
cnf(c_0_32,negated_conjecture,
antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]) ).
cnf(c_0_33,axiom,
multiplication(one,X1) = X1,
multiplicative_left_identity ).
cnf(c_0_34,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_25]) ).
cnf(c_0_35,negated_conjecture,
multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_32]),c_0_33]) ).
cnf(c_0_36,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_33]) ).
cnf(c_0_37,negated_conjecture,
multiplication(antidomain(sK1_goals_X1),addition(antidomain(antidomain(sK2_goals_X0)),X1)) = multiplication(antidomain(sK1_goals_X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_35]),c_0_25]) ).
cnf(c_0_38,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_18]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
goals_1 ).
cnf(c_0_40,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_17]) ).
cnf(c_0_41,negated_conjecture,
multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK1_goals_X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_23]),c_0_18]),c_0_38]) ).
cnf(c_0_42,negated_conjecture,
addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)) != antidomain(sK2_goals_X0),
inference(rw,[status(thm)],[c_0_39,c_0_17]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_17]),c_0_30]),c_0_33]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE090-10 : TPTP v9.2.1. Released v7.3.0.
% 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
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:30:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.24/3.34 % Version : CSE_E---1.7
% 4.24/3.34 % Problem : theBenchmark.p
% 4.24/3.34 % SZS status Unsatisfiable for theBenchmark.p
% 4.24/3.34 % SZS output start CNFRefutation
% See solution above
% 4.24/3.35 % Total time : 2.372s
%------------------------------------------------------------------------------