%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 01:00:16 PM UTC 2026
% Result : Unsatisfiable 1.88s 0.97s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of formulae : 88 ( 88 unt; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 116 ( 0 sgn 116 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
fof(f3,axiom,
! [X0] : add(X0,inverse(X0)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
fof(f4,axiom,
! [X2,X0,X1] : pixley(X0,X1,X2) = add(multiply(X0,inverse(X1)),add(multiply(X0,X2),multiply(inverse(X1),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley_defn) ).
fof(f5,axiom,
! [X0,X1] : pixley(X0,X0,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
fof(f6,axiom,
! [X0,X1] : pixley(X0,X1,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
fof(f7,axiom,
! [X0,X1] : pixley(X0,X1,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3) ).
fof(f8,negated_conjecture,
add(multiply(a,b),b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_add_multiply) ).
fof(f9,plain,
b != add(multiply(a,b),b),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),add(multiply(X0,X1),multiply(inverse(X0),X1))) = X1,
inference(definition_unfolding,[],[f5,f4]) ).
fof(f11,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),add(multiply(X0,X1),multiply(inverse(X1),X1))) = X0,
inference(definition_unfolding,[],[f6,f4]) ).
fof(f12,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),add(multiply(X0,X0),multiply(inverse(X1),X0))) = X0,
inference(definition_unfolding,[],[f7,f4]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X1) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(X1,add(X0,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i] : add(X0,inverse(X0)) = n1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X0)),add(multiply(X0,X1),multiply(inverse(X0),X1))) = X1,
inference(cnf_transformation,[],[f10]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X1)),add(multiply(X0,X1),multiply(inverse(X1),X1))) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X1)),add(multiply(X0,X0),multiply(inverse(X1),X0))) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_63,negated_conjecture,
add(multiply(a,b),b) != b,
inference(cnf_transformation,[],[f9]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X1)),multiply(X0,add(X0,inverse(X1)))) = X0,
inference(demodulation,[status(thm)],[c_62,c_58]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X1)),multiply(X1,add(X0,inverse(X1)))) = X0,
inference(demodulation,[status(thm)],[c_61,c_58]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X0)),multiply(X1,n1)) = X1,
inference(demodulation,[status(thm)],[c_60,c_58,c_59]) ).
tcf(c_134,plain,
! [X0: $i] : multiply(n1,inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[c_59,c_57]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X0,add(X0,inverse(X1)))) = multiply(X0,add(X0,inverse(X1))),
inference(superposition,[status(thm)],[c_82,c_57]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,add(X0,inverse(X1)))) = multiply(X1,add(X0,inverse(X1))),
inference(superposition,[status(thm)],[c_83,c_57]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X0)),n1) = add(X1,n1),
inference(superposition,[status(thm)],[c_57,c_84]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : add(X0,n1) = add(X1,n1),
inference(superposition,[status(thm)],[c_140,c_140]) ).
tcf(c_158,plain,
! [X0: $i] : add(inverse(X0),multiply(X0,add(n1,inverse(X0)))) = n1,
inference(superposition,[status(thm)],[c_134,c_83]) ).
tcf(c_160,plain,
! [X0: $i] : add(inverse(n1),multiply(X0,n1)) = X0,
inference(superposition,[status(thm)],[c_134,c_84]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(add(X1,X0),X2)) = add(X0,multiply(X2,X0)),
inference(superposition,[status(thm)],[c_57,c_58]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X1,inverse(X0))) = multiply(inverse(X0),add(n1,X1)),
inference(superposition,[status(thm)],[c_134,c_58]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(X1,add(X2,X0))) = add(multiply(X1,X0),X0),
inference(superposition,[status(thm)],[c_57,c_58]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X1)),inverse(X1)) = multiply(inverse(X1),add(X0,n1)),
inference(superposition,[status(thm)],[c_134,c_58]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,add(X1,X2)),multiply(X2,X0)) = multiply(X2,X0),
inference(superposition,[status(thm)],[c_58,c_57]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,multiply(X1,add(X1,inverse(X2)))),multiply(X1,add(X1,inverse(X2)))) = multiply(multiply(X1,add(X1,inverse(X2))),add(X0,X1)),
inference(superposition,[status(thm)],[c_135,c_58]) ).
tcf(c_203,plain,
! [X0: $i] : multiply(inverse(X0),add(n1,n1)) = add(inverse(X0),inverse(X0)),
inference(superposition,[status(thm)],[c_134,c_184]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),add(X1,n1)) = add(inverse(X0),inverse(X0)),
inference(superposition,[status(thm)],[c_152,c_203]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(add(X1,X0)),X0)) = multiply(X0,n1),
inference(superposition,[status(thm)],[c_59,c_183]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : add(X0,multiply(n1,X0)) = multiply(X0,add(X1,n1)),
inference(superposition,[status(thm)],[c_152,c_183]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,n1),multiply(inverse(X1),X0)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_59,c_189]) ).
tcf(c_708,plain,
! [X0: $i,X1: $i] : multiply(n1,multiply(inverse(X0),add(X1,n1))) = multiply(inverse(X0),add(X1,n1)),
inference(superposition,[status(thm)],[c_57,c_606]) ).
tcf(c_752,plain,
! [X0: $i] : multiply(n1,add(inverse(X0),inverse(X0))) = add(inverse(X0),inverse(X0)),
inference(superposition,[status(thm)],[c_217,c_708]) ).
tcf(c_783,plain,
multiply(inverse(n1),add(inverse(n1),inverse(n1))) = add(inverse(n1),inverse(n1)),
inference(superposition,[status(thm)],[c_752,c_136]) ).
tcf(c_784,plain,
add(multiply(inverse(n1),inverse(n1)),add(inverse(n1),inverse(n1))) = inverse(n1),
inference(superposition,[status(thm)],[c_752,c_83]) ).
tcf(c_805,plain,
add(multiply(multiply(inverse(n1),inverse(n1)),inverse(n1)),inverse(n1)) = multiply(inverse(n1),inverse(n1)),
inference(superposition,[status(thm)],[c_784,c_186]) ).
tcf(c_857,plain,
add(inverse(n1),inverse(n1)) = multiply(inverse(n1),inverse(n1)),
inference(demodulation,[status(thm)],[c_805,c_187,c_217]) ).
tcf(c_859,plain,
add(multiply(inverse(n1),inverse(n1)),multiply(inverse(n1),inverse(n1))) = inverse(n1),
inference(demodulation,[status(thm)],[c_784,c_857]) ).
tcf(c_860,plain,
multiply(inverse(n1),multiply(inverse(n1),inverse(n1))) = multiply(inverse(n1),inverse(n1)),
inference(demodulation,[status(thm)],[c_783,c_857]) ).
tcf(c_951,plain,
multiply(inverse(n1),inverse(n1)) = inverse(n1),
inference(demodulation,[status(thm)],[c_859,c_58,c_857,c_860]) ).
tcf(c_955,plain,
add(inverse(n1),inverse(n1)) = inverse(n1),
inference(demodulation,[status(thm)],[c_857,c_951]) ).
tcf(c_964,plain,
multiply(inverse(n1),add(n1,inverse(n1))) = add(inverse(n1),inverse(n1)),
inference(superposition,[status(thm)],[c_951,c_184]) ).
tcf(c_967,plain,
multiply(inverse(n1),add(n1,inverse(n1))) = inverse(n1),
inference(light_normalisation,[status(thm)],[c_964,c_955]) ).
tcf(c_1033,plain,
multiply(inverse(n1),n1) = inverse(n1),
inference(demodulation,[status(thm)],[c_967,c_59]) ).
tcf(c_1034,plain,
! [X0: $i] : multiply(multiply(n1,add(X0,inverse(n1))),inverse(n1)) = inverse(n1),
inference(superposition,[status(thm)],[c_1033,c_189]) ).
tcf(c_1035,plain,
! [X0: $i] : add(inverse(n1),multiply(X0,n1)) = multiply(n1,add(inverse(n1),X0)),
inference(superposition,[status(thm)],[c_1033,c_58]) ).
tcf(c_1045,plain,
! [X0: $i] : multiply(n1,add(inverse(n1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1035,c_160]) ).
tcf(c_1056,plain,
multiply(n1,n1) = inverse(inverse(n1)),
inference(superposition,[status(thm)],[c_59,c_1045]) ).
tcf(c_1063,plain,
! [X0: $i] : multiply(X0,n1) = multiply(n1,X0),
inference(superposition,[status(thm)],[c_160,c_1045]) ).
tcf(c_1069,plain,
! [X0: $i,X1: $i] : multiply(multiply(add(inverse(n1),X0),add(X1,n1)),X0) = X0,
inference(superposition,[status(thm)],[c_1045,c_189]) ).
tcf(c_1076,plain,
add(n1,multiply(n1,n1)) = n1,
inference(superposition,[status(thm)],[c_1045,c_295]) ).
tcf(c_1275,plain,
add(multiply(n1,n1),multiply(inverse(n1),add(n1,multiply(n1,n1)))) = n1,
inference(superposition,[status(thm)],[c_1056,c_158]) ).
tcf(c_1286,plain,
add(multiply(n1,n1),multiply(inverse(n1),n1)) = n1,
inference(light_normalisation,[status(thm)],[c_1275,c_1076]) ).
tcf(c_1305,plain,
! [X0: $i,X1: $i] : add(multiply(n1,X0),multiply(X1,n1)) = multiply(n1,add(X0,X1)),
inference(superposition,[status(thm)],[c_1063,c_58]) ).
tcf(c_1311,plain,
! [X0: $i] : add(inverse(n1),multiply(n1,X0)) = X0,
inference(superposition,[status(thm)],[c_1063,c_160]) ).
tcf(c_1454,plain,
multiply(n1,n1) = n1,
inference(demodulation,[status(thm)],[c_1286,c_59,c_1305]) ).
tcf(c_1456,plain,
inverse(inverse(n1)) = n1,
inference(demodulation,[status(thm)],[c_1056,c_1454]) ).
tcf(c_1460,plain,
! [X0: $i] : add(multiply(X0,inverse(X0)),n1) = n1,
inference(superposition,[status(thm)],[c_1454,c_84]) ).
tcf(c_1489,plain,
! [X0: $i] : add(X0,n1) = n1,
inference(superposition,[status(thm)],[c_1460,c_152]) ).
tcf(c_1498,plain,
! [X0: $i] : multiply(multiply(add(inverse(n1),X0),n1),X0) = X0,
inference(demodulation,[status(thm)],[c_1069,c_1489]) ).
tcf(c_1551,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_1498,c_1045,c_1063]) ).
tcf(c_1556,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(X0,add(X0,X1)),
inference(superposition,[status(thm)],[c_1551,c_58]) ).
tcf(c_1557,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X1) = multiply(X1,add(X0,X1)),
inference(superposition,[status(thm)],[c_1551,c_58]) ).
tcf(c_1571,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,inverse(add(X1,X0)))) = multiply(X0,n1),
inference(demodulation,[status(thm)],[c_294,c_1556]) ).
tcf(c_1575,plain,
multiply(b,add(a,b)) != b,
inference(demodulation,[status(thm)],[c_63,c_1557]) ).
tcf(c_1692,plain,
! [X0: $i] : add(multiply(X0,n1),multiply(inverse(n1),add(X0,n1))) = X0,
inference(superposition,[status(thm)],[c_1456,c_83]) ).
tcf(c_1694,plain,
! [X0: $i] : add(multiply(X0,n1),multiply(inverse(n1),n1)) = X0,
inference(light_normalisation,[status(thm)],[c_1692,c_1489]) ).
tcf(c_1987,plain,
! [X0: $i] : multiply(n1,add(X0,inverse(n1))) = X0,
inference(demodulation,[status(thm)],[c_1694,c_58]) ).
tcf(c_1988,plain,
! [X0: $i] : multiply(X0,inverse(n1)) = inverse(n1),
inference(demodulation,[status(thm)],[c_1034,c_1987]) ).
tcf(c_2000,plain,
! [X0: $i] : add(multiply(X0,inverse(n1)),X0) = X0,
inference(superposition,[status(thm)],[c_1987,c_83]) ).
tcf(c_2003,plain,
! [X0: $i] : add(inverse(n1),X0) = X0,
inference(light_normalisation,[status(thm)],[c_2000,c_1988]) ).
tcf(c_2008,plain,
! [X0: $i] : multiply(n1,X0) = X0,
inference(demodulation,[status(thm)],[c_1311,c_2003]) ).
tcf(c_2009,plain,
! [X0: $i] : multiply(X0,n1) = X0,
inference(demodulation,[status(thm)],[c_1063,c_2008]) ).
tcf(c_2104,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X1) = multiply(X1,add(X0,n1)),
inference(superposition,[status(thm)],[c_2008,c_58]) ).
tcf(c_2116,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X1) = multiply(X1,n1),
inference(light_normalisation,[status(thm)],[c_2104,c_1489,c_1557]) ).
tcf(c_2275,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,inverse(add(X1,X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_1571,c_2009]) ).
tcf(c_2345,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,add(X0,inverse(X1))),add(X2,X0)) = multiply(X0,add(X0,inverse(X1))),
inference(demodulation,[status(thm)],[c_199,c_2009,c_2116]) ).
tcf(c_2350,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_2275,c_2345]) ).
tcf(c_2392,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1575,c_2350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 06:34:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running UEQ theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.03/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 1.88/0.97 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.88/0.97 % SZS status Started for theBenchmark.p
% 1.88/0.97 % SZS status Unsatisfiable for theBenchmark.p
% 1.88/0.97
% 1.88/0.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.88/0.97
% 1.88/0.97 % ------ iProver source info
% 1.88/0.97
% 1.88/0.97 % git: date: 2026-07-19 20:42:38 +0200
% 1.88/0.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.88/0.97 % git: non_committed_changes: false
% 1.88/0.97
% 1.88/0.97 % ------ Parsing...% successful
% 1.88/0.97
% 1.88/0.97
% 1.88/0.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.88/0.97
% 1.88/0.97 % ------ Preprocessing... sup_sim: 3 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.88/0.97
% 1.88/0.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.88/0.97
% 1.88/0.97 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.88/0.97 % ------ Proving...
% 1.88/0.97 % ------ Problem Properties
% 1.88/0.97
% 1.88/0.97 %
% 1.88/0.97 % clauses 7
% 1.88/0.97 % conjectures 1
% 1.88/0.97 % EPR 0
% 1.88/0.97 % Horn 7
% 1.88/0.97 % unary 7
% 1.88/0.97 % binary 0
% 1.88/0.97 % lits 7
% 1.88/0.97 % lits eq 7
% 1.88/0.97 % fd_pure 0
% 1.88/0.97 % fd_pseudo 0
% 1.88/0.97 % fd_cond 0
% 1.88/0.97 % fd_pseudo_cond 0
% 1.88/0.97 % AC symbols 0
% 1.88/0.97
% 1.88/0.97 % ------ Input Options Time Limit: Unbounded
% 1.88/0.97
% 1.88/0.97
% 1.88/0.97 % ------
% 1.88/0.97 % Current options:
% 1.88/0.97 % ------
% 1.88/0.97
% 1.88/0.97
% 1.88/0.97 %
% 1.88/0.97
% 1.88/0.97 % ------ Proving...
% 1.88/0.97 %
% 1.88/0.97
% 1.88/0.97 % SZS status Unsatisfiable for theBenchmark.p
% 1.88/0.97
% 1.88/0.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.88/0.97
% 1.88/0.97
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