%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG029-3 : TPTP v9.3.1. Bugfixed v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:38:15 PM UTC 2026
% Result : Unsatisfiable 2.01s 34.16s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 107 ( 107 unt; 0 def)
% Number of atoms : 107 ( 106 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 285 ( 0 sgn 285 !; 0 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',left_additive_identity) ).
fof(f4,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',right_multiplicative_zero) ).
fof(f5,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',add_inverse) ).
fof(f7,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',sum_of_inverses) ).
fof(f9,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',additive_inverse_additive_inverse) ).
fof(f10,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',multiply_over_add1) ).
fof(f12,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',right_alternative) ).
fof(f14,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',inverse_product1) ).
fof(f15,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',inverse_product2) ).
fof(f16,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(reorient_equations,[],[f15]) ).
fof(f19,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',commutativity_for_addition) ).
fof(f20,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',associativity_for_addition) ).
fof(f24,axiom,
! [X2,X0,X1] : multiply(multiply(X0,multiply(X1,X0)),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_moufang) ).
fof(f25,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator) ).
fof(f28,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = additive_inverse(associator(X1,X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
fof(f29,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = additive_inverse(associator(X2,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry2) ).
fof(f30,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_middle_law) ).
fof(f31,plain,
! [X2,X0,X1] : add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))) = additive_inverse(add(multiply(multiply(X1,X0),X2),additive_inverse(multiply(X1,multiply(X0,X2))))),
inference(definition_unfolding,[],[f28,f25,f25]) ).
fof(f32,plain,
! [X2,X0,X1] : add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))) = additive_inverse(add(multiply(multiply(X2,X1),X0),additive_inverse(multiply(X2,multiply(X1,X0))))),
inference(definition_unfolding,[],[f29,f25,f25]) ).
tcf(c_73,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(cnf_transformation,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i] : add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[],[f7]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),additive_inverse(X1)) = additive_inverse(add(X0,X1)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_78,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f19]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,X0)),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(cnf_transformation,[],[f24]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2))))) = add(multiply(multiply(X1,X0),X2),additive_inverse(multiply(X1,multiply(X0,X2)))),
inference(cnf_transformation,[],[f31]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2))))) = add(multiply(multiply(X2,X1),X0),additive_inverse(multiply(X2,multiply(X1,X0)))),
inference(cnf_transformation,[],[f32]) ).
tcf(c_95,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_112,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_76,c_87,c_86]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(light_normalisation,[status(thm)],[c_83,c_84]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,additive_inverse(X2))))) = add(multiply(multiply(X2,X1),X0),multiply(X2,multiply(X1,additive_inverse(X0)))),
inference(demodulation,[status(thm)],[c_94,c_84]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,additive_inverse(X2)))) = add(multiply(multiply(X1,X2),X0),multiply(X1,multiply(X2,additive_inverse(X0)))),
inference(demodulation,[status(thm)],[c_93,c_84,c_165]) ).
tcf(c_1005,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X2,X1)),
inference(superposition,[status(thm)],[c_79,c_86]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,additive_inverse(X1)),X2) = multiply(multiply(X0,X1),additive_inverse(X2)),
inference(superposition,[status(thm)],[c_84,c_164]) ).
tcf(c_7885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,X1),add(multiply(X0,X2),X3)) = add(multiply(X0,add(X2,X1)),X3),
inference(superposition,[status(thm)],[c_1005,c_87]) ).
tcf(c_21084,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_87,c_86]) ).
tcf(c_21090,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(superposition,[status(thm)],[c_73,c_86]) ).
tcf(c_21106,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_112,c_87]) ).
tcf(c_21108,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_21106,c_73]) ).
tcf(c_21117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,X1),add(multiply(X0,X2),X3)) = add(multiply(X0,add(X1,X2)),X3),
inference(superposition,[status(thm)],[c_79,c_87]) ).
tcf(c_21154,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_78,c_21108]) ).
tcf(c_21161,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(theory_normalisation,[status(thm)],[c_21154,c_87,c_86]) ).
tcf(c_21186,plain,
! [X0: $i,X1: $i] : additive_inverse(add(X0,additive_inverse(X1))) = add(additive_inverse(X0),X1),
inference(superposition,[status(thm)],[c_78,c_77]) ).
tcf(c_21190,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),additive_inverse(X1)) = additive_inverse(add(X1,X0)),
inference(superposition,[status(thm)],[c_77,c_86]) ).
tcf(c_21193,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_77,c_21108]) ).
tcf(c_21194,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_77,c_21161]) ).
tcf(c_21208,plain,
! [X0: $i,X1: $i] : additive_inverse(add(X0,additive_inverse(X1))) = add(X1,additive_inverse(X0)),
inference(superposition,[status(thm)],[c_21161,c_21193]) ).
tcf(c_21284,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(X0,multiply(X1,multiply(X0,X2))),multiply(X0,multiply(multiply(X1,X0),additive_inverse(X2))))) = add(multiply(multiply(X2,multiply(X1,X0)),X0),multiply(X2,multiply(multiply(X1,X0),additive_inverse(X0)))),
inference(superposition,[status(thm)],[c_91,c_165]) ).
tcf(c_21296,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(additive_inverse(X0),X1),X2),multiply(additive_inverse(X0),multiply(X1,additive_inverse(X2)))) = additive_inverse(add(multiply(multiply(X2,X1),additive_inverse(X0)),multiply(X2,multiply(X1,X0)))),
inference(superposition,[status(thm)],[c_78,c_165]) ).
tcf(c_21311,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,multiply(X1,additive_inverse(X2))),add(multiply(multiply(X2,X1),X0),multiply(X2,multiply(X1,additive_inverse(X0))))) = additive_inverse(multiply(multiply(X0,X1),X2)),
inference(superposition,[status(thm)],[c_165,c_21194]) ).
tcf(c_21315,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,X1),X2),add(multiply(X2,multiply(X1,additive_inverse(X0))),multiply(X0,multiply(X1,additive_inverse(X2))))) = additive_inverse(multiply(multiply(X2,X1),X0)),
inference(theory_normalisation,[status(thm)],[c_21311,c_87,c_86]) ).
tcf(c_21316,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,X1),X2),add(multiply(X2,multiply(X1,additive_inverse(X0))),multiply(X0,multiply(X1,additive_inverse(X2))))) = multiply(multiply(X2,X1),additive_inverse(X0)),
inference(demodulation,[status(thm)],[c_21315,c_84]) ).
tcf(c_21319,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(additive_inverse(X0),X1),X2),multiply(additive_inverse(X0),multiply(X1,additive_inverse(X2)))) = additive_inverse(add(multiply(X2,multiply(X1,X0)),multiply(multiply(X2,X1),additive_inverse(X0)))),
inference(theory_normalisation,[status(thm)],[c_21296,c_87,c_86]) ).
tcf(c_21320,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),additive_inverse(X2)))) = add(multiply(X2,multiply(X1,X0)),multiply(multiply(X2,X1),additive_inverse(X0))),
inference(demodulation,[status(thm)],[c_21319,c_78,c_84,c_86,c_164,c_1012]) ).
tcf(c_21327,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,X1),multiply(X2,X0)),multiply(X0,multiply(X1,multiply(X2,additive_inverse(X0))))) = multiply(X0,additive_inverse(add(multiply(X2,multiply(X0,X1)),multiply(multiply(X2,X0),additive_inverse(X1))))),
inference(demodulation,[status(thm)],[c_21284,c_79,c_84,c_166]) ).
tcf(c_21406,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),additive_inverse(X1)) = additive_inverse(multiply(X0,multiply(X1,X1))),
inference(superposition,[status(thm)],[c_81,c_84]) ).
tcf(c_21416,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),additive_inverse(X1)) = multiply(X0,multiply(X1,additive_inverse(X1))),
inference(demodulation,[status(thm)],[c_21406,c_84]) ).
tcf(c_21459,plain,
! [X0: $i,X1: $i] : additive_inverse(add(additive_inverse(X0),X1)) = add(additive_inverse(X1),X0),
inference(superposition,[status(thm)],[c_86,c_21186]) ).
tcf(c_21504,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,additive_inverse(X1)),additive_inverse(X2)) = additive_inverse(add(X2,multiply(X0,X1))),
inference(superposition,[status(thm)],[c_84,c_21190]) ).
tcf(c_21506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : additive_inverse(add(X0,add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X3)))))) = add(add(multiply(multiply(X3,X2),X1),multiply(X3,multiply(X2,additive_inverse(X1)))),additive_inverse(X0)),
inference(superposition,[status(thm)],[c_165,c_21190]) ).
tcf(c_21510,plain,
! [X0: $i,X1: $i,X2: $i] : add(additive_inverse(X0),multiply(X1,additive_inverse(X2))) = additive_inverse(add(multiply(X1,X2),X0)),
inference(superposition,[status(thm)],[c_84,c_21190]) ).
tcf(c_21545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : additive_inverse(add(X0,add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X3)))))) = add(multiply(multiply(X3,X2),X1),add(multiply(X3,multiply(X2,additive_inverse(X1))),additive_inverse(X0))),
inference(theory_normalisation,[status(thm)],[c_21506,c_87,c_86]) ).
tcf(c_21553,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(X0,add(X1,additive_inverse(X2)))) = add(X2,additive_inverse(add(X0,X1))),
inference(superposition,[status(thm)],[c_87,c_21208]) ).
tcf(c_21558,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(X0,multiply(X1,additive_inverse(X2)))) = add(multiply(X1,X2),additive_inverse(X0)),
inference(superposition,[status(thm)],[c_84,c_21208]) ).
tcf(c_21618,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(X0,additive_inverse(X1)),X2)) = add(additive_inverse(X2),multiply(X0,X1)),
inference(superposition,[status(thm)],[c_84,c_21459]) ).
tcf(c_21816,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,multiply(X1,X1)),X2),multiply(multiply(X0,X1),multiply(X1,additive_inverse(X2)))) = add(multiply(multiply(X2,multiply(X0,X1)),X1),multiply(X2,multiply(multiply(X0,X1),additive_inverse(X1)))),
inference(superposition,[status(thm)],[c_81,c_166]) ).
tcf(c_21849,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,additive_inverse(X2))))) = add(multiply(multiply(X1,X0),X2),multiply(X1,multiply(X0,additive_inverse(X2)))),
inference(superposition,[status(thm)],[c_166,c_165]) ).
tcf(c_21886,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,multiply(X1,X1)),X2),multiply(multiply(X0,X1),multiply(X1,additive_inverse(X2)))) = multiply(X1,add(multiply(X2,multiply(X1,X0)),multiply(multiply(X2,X1),additive_inverse(X0)))),
inference(demodulation,[status(thm)],[c_21816,c_84,c_166,c_21320,c_21327]) ).
tcf(c_22053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(add(multiply(X0,X1),X2),multiply(X0,X3)) = add(multiply(X0,add(X1,X3)),X2),
inference(superposition,[status(thm)],[c_7885,c_86]) ).
tcf(c_22068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,X1),add(X2,multiply(X0,X3))) = add(multiply(X0,add(X1,X3)),X2),
inference(theory_normalisation,[status(thm)],[c_22053,c_87,c_86]) ).
tcf(c_22451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,multiply(X1,additive_inverse(X2))),additive_inverse(X3)) = additive_inverse(add(X3,multiply(X0,multiply(X1,X2)))),
inference(superposition,[status(thm)],[c_84,c_21504]) ).
tcf(c_22828,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(additive_inverse(X1),additive_inverse(X1))),X2) = multiply(multiply(multiply(X0,additive_inverse(X1)),X1),additive_inverse(X2)),
inference(superposition,[status(thm)],[c_81,c_1012]) ).
tcf(c_22857,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(multiply(X0,X1),additive_inverse(X2)),multiply(X0,multiply(additive_inverse(X1),additive_inverse(X2))))) = add(multiply(multiply(X2,additive_inverse(X1)),X0),multiply(X2,multiply(additive_inverse(X1),additive_inverse(X0)))),
inference(superposition,[status(thm)],[c_1012,c_165]) ).
tcf(c_22886,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,additive_inverse(X1))),additive_inverse(X2)) = multiply(multiply(X0,multiply(X1,X1)),X2),
inference(demodulation,[status(thm)],[c_22828,c_78,c_164,c_1012,c_21416]) ).
tcf(c_22896,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,additive_inverse(X2)))) = add(multiply(X2,multiply(X1,X0)),multiply(multiply(X2,X1),additive_inverse(X0))),
inference(demodulation,[status(thm)],[c_22857,c_78,c_84,c_86,c_164,c_1012,c_21618]) ).
tcf(c_22929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : additive_inverse(add(X0,add(X1,multiply(X2,additive_inverse(X3))))) = add(multiply(X2,X3),additive_inverse(add(X0,X1))),
inference(superposition,[status(thm)],[c_84,c_21553]) ).
tcf(c_23030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : additive_inverse(add(add(X0,multiply(X1,additive_inverse(X2))),X3)) = add(multiply(X1,X2),additive_inverse(add(X3,X0))),
inference(superposition,[status(thm)],[c_86,c_22929]) ).
tcf(c_23056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : additive_inverse(add(X0,add(X1,multiply(X2,multiply(X3,additive_inverse(X4)))))) = add(multiply(X2,multiply(X3,X4)),additive_inverse(add(X0,X1))),
inference(superposition,[status(thm)],[c_84,c_22929]) ).
tcf(c_23102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : additive_inverse(add(X0,add(multiply(X1,additive_inverse(X2)),X3))) = add(multiply(X1,X2),additive_inverse(add(X3,X0))),
inference(theory_normalisation,[status(thm)],[c_23030,c_87,c_86]) ).
tcf(c_23230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(additive_inverse(add(multiply(X0,additive_inverse(X1)),X2)),X3) = add(multiply(X0,X1),additive_inverse(add(X2,additive_inverse(X3)))),
inference(superposition,[status(thm)],[c_23102,c_21459]) ).
tcf(c_23246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,X1),add(X2,additive_inverse(X3))) = add(additive_inverse(X3),add(multiply(X0,X1),X2)),
inference(demodulation,[status(thm)],[c_23230,c_87,c_21208,c_21618]) ).
tcf(c_23835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,X1),add(multiply(multiply(X2,X3),X0),multiply(X2,multiply(X3,additive_inverse(X0))))) = add(multiply(X0,add(X1,multiply(X2,additive_inverse(X3)))),multiply(multiply(X0,X2),X3)),
inference(superposition,[status(thm)],[c_166,c_22068]) ).
tcf(c_23912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,X1),add(multiply(multiply(X2,X3),X0),multiply(X2,multiply(X3,additive_inverse(X0))))) = add(multiply(multiply(X0,X2),X3),multiply(X0,add(X1,multiply(X2,additive_inverse(X3))))),
inference(theory_normalisation,[status(thm)],[c_23835,c_87,c_86]) ).
tcf(c_25341,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(multiply(X0,X1),additive_inverse(X2)),multiply(X0,multiply(X1,X2)))) = add(multiply(multiply(X1,X0),additive_inverse(X2)),multiply(X1,multiply(X0,X2))),
inference(superposition,[status(thm)],[c_78,c_21849]) ).
tcf(c_25412,plain,
! [X0: $i,X1: $i,X2: $i] : additive_inverse(add(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),additive_inverse(X2)))) = add(multiply(X1,multiply(X0,X2)),multiply(multiply(X1,X0),additive_inverse(X2))),
inference(theory_normalisation,[status(thm)],[c_25341,c_87,c_86]) ).
tcf(c_25413,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,additive_inverse(X2)))) = add(multiply(X1,multiply(X0,X2)),multiply(multiply(X1,X0),additive_inverse(X2))),
inference(demodulation,[status(thm)],[c_25412,c_84,c_21558]) ).
tcf(c_25606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(add(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),additive_inverse(X2))),X3) = add(multiply(multiply(X1,X0),X2),add(multiply(X1,multiply(X0,additive_inverse(X2))),X3)),
inference(superposition,[status(thm)],[c_25413,c_87]) ).
tcf(c_25621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(multiply(X0,X1),X2),add(multiply(X0,multiply(X1,additive_inverse(X2))),X3)) = add(multiply(X1,multiply(X0,X2)),add(multiply(multiply(X1,X0),additive_inverse(X2)),X3)),
inference(theory_normalisation,[status(thm)],[c_25606,c_87,c_86]) ).
tcf(c_25673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,multiply(X1,X2)),additive_inverse(add(X3,multiply(multiply(X0,X1),X2)))) = add(multiply(X1,multiply(X2,X0)),additive_inverse(add(X3,multiply(multiply(X1,X2),X0)))),
inference(demodulation,[status(thm)],[c_21545,c_21504,c_25621,c_23056]) ).
tcf(c_25791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(additive_inverse(X0),multiply(X1,X2)),additive_inverse(add(additive_inverse(X3),multiply(multiply(additive_inverse(X0),X1),X2)))) = add(multiply(X1,multiply(X2,additive_inverse(X0))),additive_inverse(additive_inverse(add(multiply(multiply(X1,X2),X0),X3)))),
inference(superposition,[status(thm)],[c_21510,c_25673]) ).
tcf(c_25960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(multiply(X0,X1),X2),add(X3,multiply(X0,multiply(X1,additive_inverse(X2))))) = add(multiply(X0,multiply(X2,X1)),add(multiply(multiply(X0,X2),additive_inverse(X1)),X3)),
inference(demodulation,[status(thm)],[c_25791,c_78,c_84,c_164,c_21084,c_1012,c_21459,c_25621,c_22451,c_23246]) ).
tcf(c_26908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,X1),add(multiply(multiply(X2,X3),X0),multiply(X2,multiply(X3,additive_inverse(X0))))) = add(multiply(X0,add(X1,multiply(X3,X2))),multiply(multiply(X0,X3),additive_inverse(X2))),
inference(superposition,[status(thm)],[c_22896,c_21117]) ).
tcf(c_26959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(X0,X1),add(multiply(multiply(X2,X3),X0),multiply(X2,multiply(X3,additive_inverse(X0))))) = add(multiply(multiply(X0,X3),additive_inverse(X2)),multiply(X0,add(X1,multiply(X3,X2)))),
inference(theory_normalisation,[status(thm)],[c_26908,c_87,c_86]) ).
tcf(c_26960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : add(multiply(multiply(X0,X1),additive_inverse(X2)),multiply(X0,add(X3,multiply(X1,X2)))) = add(multiply(multiply(X0,X2),X1),multiply(X0,add(X3,multiply(X2,additive_inverse(X1))))),
inference(demodulation,[status(thm)],[c_26959,c_23912]) ).
tcf(c_56984,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,multiply(X1,X2)),add(multiply(X1,multiply(X2,additive_inverse(X0))),multiply(multiply(X0,X1),additive_inverse(X2)))) = multiply(multiply(X1,X2),additive_inverse(X0)),
inference(demodulation,[status(thm)],[c_21316,c_86,c_25960]) ).
tcf(c_57148,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(multiply(X0,X1),multiply(additive_inverse(X1),X2)),add(multiply(additive_inverse(X1),multiply(X2,additive_inverse(multiply(X0,X1)))),multiply(multiply(X0,multiply(X1,additive_inverse(X1))),additive_inverse(X2)))) = multiply(multiply(additive_inverse(X1),X2),additive_inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[c_21416,c_56984]) ).
tcf(c_57331,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),multiply(X2,X0)) = multiply(X0,multiply(multiply(X1,X2),X0)),
inference(demodulation,[status(thm)],[c_57148,c_75,c_78,c_79,c_84,c_86,c_112,c_164,c_21084,c_21090,c_1012,c_21117,c_21886,c_22886,c_26960]) ).
tcf(c_57448,plain,
multiply(cx,multiply(multiply(cy,cz),cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(demodulation,[status(thm)],[c_95,c_57331]) ).
tcf(c_57449,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_57448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG029-3 : TPTP v9.3.1. Bugfixed v2.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.46 % Computer : n013.cluster.edu
% 0.16/0.46 % Model : x86_64 x86_64
% 0.16/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.46 % Memory : 8046.5625MB
% 0.16/0.46 % OS : Linux 6.8.0-71-generic
% 0.16/0.46 % CPULimit : 300
% 0.16/0.46 % WCLimit : 300
% 0.16/0.46 % DateTime : Thu Sep 24 07:51:36 UTC 2026
% 0.16/0.47 % CPUTime :
% 0.16/0.47 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.21/0.52 Running first-order theorem proving
% 0.21/0.52 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.54
% 0.21/0.54 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.54
% 0.21/0.54 % Detected problem language: tptp
% 0.21/0.56 % Proving...
% 2.01/34.16 % SZS status Started for theBenchmark.p
% 2.01/34.16 % SZS status Unsatisfiable for theBenchmark.p
% 2.01/34.16
% 2.01/34.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.01/34.16
% 2.01/34.16 % ------ iProver source info
% 2.01/34.16
% 2.01/34.16 % git: date: 2026-07-19 20:42:38 +0200
% 2.01/34.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.01/34.16 % git: non_committed_changes: false
% 2.01/34.16
% 2.01/34.16 % ------ Parsing...% successful
% 2.01/34.16
% 2.01/34.16
% 2.01/34.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.01/34.16
% 2.01/34.16 % ------ Preprocessing... sup_sim: 3 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.01/34.16
% 2.01/34.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.01/34.16
% 2.01/34.16 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.01/34.16 % ------ Proving...
% 2.01/34.16 % ------ Problem Properties
% 2.01/34.16
% 2.01/34.16 %
% 2.01/34.16 % clauses 23
% 2.01/34.16 % conjectures 1
% 2.01/34.16 % EPR 0
% 2.01/34.16 % Horn 23
% 2.01/34.16 % unary 21
% 2.01/34.16 % binary 2
% 2.01/34.16 % lits 25
% 2.01/34.16 % lits eq 25
% 2.01/34.16 % fd_pure 0
% 2.01/34.16 % fd_pseudo 0
% 2.01/34.16 % fd_cond 0
% 2.01/34.16 % fd_pseudo_cond 2
% 2.01/34.16 % AC symbols 1
% 2.01/34.16
% 2.01/34.16 % ------ Input Options Time Limit: Unbounded
% 2.01/34.16
% 2.01/34.16
% 2.01/34.16 % ------
% 2.01/34.16 % Current options:
% 2.01/34.16 % ------
% 2.01/34.16
% 2.01/34.16
% 2.01/34.16 %
% 2.01/34.16
% 2.01/34.16 % ------ Proving...
% 2.01/34.16 %
% 2.01/34.16
% 2.01/34.16 % SZS status Unsatisfiable for theBenchmark.p
% 2.01/34.16
% 2.01/34.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.01/34.16
% 2.01/34.16
%------------------------------------------------------------------------------