%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO025-1 : 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 2.33s 0.96s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 7
% Syntax : Number of formulae : 80 ( 80 unt; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 98 ( 0 sgn 98 !; 0 ?; 81 :)
% 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(f8,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_identity) ).
fof(f9,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),add(multiply(X0,X1),multiply(inverse(X0),X1))) = X1,
inference(definition_unfolding,[],[f5,f4]) ).
fof(f10,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),add(multiply(X0,X1),multiply(inverse(X1),X1))) = X0,
inference(definition_unfolding,[],[f6,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,[],[f9]) ).
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,[],[f10]) ).
tcf(c_63,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
inference(cnf_transformation,[],[f8]) ).
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_141,plain,
! [X0: $i] : multiply(n1,inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[c_59,c_57]) ).
tcf(c_143,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_147,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X0)),n1) = add(X1,n1),
inference(superposition,[status(thm)],[c_57,c_84]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] : add(X0,n1) = add(X1,n1),
inference(superposition,[status(thm)],[c_147,c_147]) ).
tcf(c_165,plain,
! [X0: $i] : add(inverse(X0),multiply(X0,add(n1,inverse(X0)))) = n1,
inference(superposition,[status(thm)],[c_141,c_83]) ).
tcf(c_167,plain,
! [X0: $i] : add(inverse(n1),multiply(X0,n1)) = X0,
inference(superposition,[status(thm)],[c_141,c_84]) ).
tcf(c_190,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_191,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X1,inverse(X0))) = multiply(inverse(X0),add(n1,X1)),
inference(superposition,[status(thm)],[c_141,c_58]) ).
tcf(c_193,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_194,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X1)),inverse(X1)) = multiply(inverse(X1),add(X0,n1)),
inference(superposition,[status(thm)],[c_141,c_58]) ).
tcf(c_196,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_210,plain,
! [X0: $i] : multiply(inverse(X0),add(n1,n1)) = add(inverse(X0),inverse(X0)),
inference(superposition,[status(thm)],[c_141,c_191]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),add(X1,n1)) = add(inverse(X0),inverse(X0)),
inference(superposition,[status(thm)],[c_159,c_210]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] : add(X0,multiply(n1,X0)) = multiply(X0,add(X1,n1)),
inference(superposition,[status(thm)],[c_159,c_190]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,n1),multiply(inverse(X1),X0)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_59,c_196]) ).
tcf(c_715,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_613]) ).
tcf(c_759,plain,
! [X0: $i] : multiply(n1,add(inverse(X0),inverse(X0))) = add(inverse(X0),inverse(X0)),
inference(superposition,[status(thm)],[c_224,c_715]) ).
tcf(c_790,plain,
multiply(inverse(n1),add(inverse(n1),inverse(n1))) = add(inverse(n1),inverse(n1)),
inference(superposition,[status(thm)],[c_759,c_143]) ).
tcf(c_791,plain,
add(multiply(inverse(n1),inverse(n1)),add(inverse(n1),inverse(n1))) = inverse(n1),
inference(superposition,[status(thm)],[c_759,c_83]) ).
tcf(c_812,plain,
add(multiply(multiply(inverse(n1),inverse(n1)),inverse(n1)),inverse(n1)) = multiply(inverse(n1),inverse(n1)),
inference(superposition,[status(thm)],[c_791,c_193]) ).
tcf(c_864,plain,
add(inverse(n1),inverse(n1)) = multiply(inverse(n1),inverse(n1)),
inference(demodulation,[status(thm)],[c_812,c_194,c_224]) ).
tcf(c_866,plain,
add(multiply(inverse(n1),inverse(n1)),multiply(inverse(n1),inverse(n1))) = inverse(n1),
inference(demodulation,[status(thm)],[c_791,c_864]) ).
tcf(c_867,plain,
multiply(inverse(n1),multiply(inverse(n1),inverse(n1))) = multiply(inverse(n1),inverse(n1)),
inference(demodulation,[status(thm)],[c_790,c_864]) ).
tcf(c_958,plain,
multiply(inverse(n1),inverse(n1)) = inverse(n1),
inference(demodulation,[status(thm)],[c_866,c_58,c_864,c_867]) ).
tcf(c_962,plain,
add(inverse(n1),inverse(n1)) = inverse(n1),
inference(demodulation,[status(thm)],[c_864,c_958]) ).
tcf(c_971,plain,
multiply(inverse(n1),add(n1,inverse(n1))) = add(inverse(n1),inverse(n1)),
inference(superposition,[status(thm)],[c_958,c_191]) ).
tcf(c_974,plain,
multiply(inverse(n1),add(n1,inverse(n1))) = inverse(n1),
inference(light_normalisation,[status(thm)],[c_971,c_962]) ).
tcf(c_1040,plain,
multiply(inverse(n1),n1) = inverse(n1),
inference(demodulation,[status(thm)],[c_974,c_59]) ).
tcf(c_1041,plain,
! [X0: $i] : multiply(multiply(n1,add(X0,inverse(n1))),inverse(n1)) = inverse(n1),
inference(superposition,[status(thm)],[c_1040,c_196]) ).
tcf(c_1042,plain,
! [X0: $i] : add(inverse(n1),multiply(X0,n1)) = multiply(n1,add(inverse(n1),X0)),
inference(superposition,[status(thm)],[c_1040,c_58]) ).
tcf(c_1052,plain,
! [X0: $i] : multiply(n1,add(inverse(n1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1042,c_167]) ).
tcf(c_1063,plain,
multiply(n1,n1) = inverse(inverse(n1)),
inference(superposition,[status(thm)],[c_59,c_1052]) ).
tcf(c_1070,plain,
! [X0: $i] : multiply(X0,n1) = multiply(n1,X0),
inference(superposition,[status(thm)],[c_167,c_1052]) ).
tcf(c_1083,plain,
add(n1,multiply(n1,n1)) = n1,
inference(superposition,[status(thm)],[c_1052,c_302]) ).
tcf(c_1282,plain,
add(multiply(n1,n1),multiply(inverse(n1),add(n1,multiply(n1,n1)))) = n1,
inference(superposition,[status(thm)],[c_1063,c_165]) ).
tcf(c_1293,plain,
add(multiply(n1,n1),multiply(inverse(n1),n1)) = n1,
inference(light_normalisation,[status(thm)],[c_1282,c_1083]) ).
tcf(c_1312,plain,
! [X0: $i,X1: $i] : add(multiply(n1,X0),multiply(X1,n1)) = multiply(n1,add(X0,X1)),
inference(superposition,[status(thm)],[c_1070,c_58]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X0)),multiply(n1,X1)) = X1,
inference(superposition,[status(thm)],[c_1070,c_84]) ).
tcf(c_1318,plain,
! [X0: $i] : add(inverse(n1),multiply(n1,X0)) = X0,
inference(superposition,[status(thm)],[c_1070,c_167]) ).
tcf(c_1369,plain,
! [X0: $i] : add(inverse(n1),inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[c_141,c_1318]) ).
tcf(c_1461,plain,
multiply(n1,n1) = n1,
inference(demodulation,[status(thm)],[c_1293,c_59,c_1312]) ).
tcf(c_1463,plain,
inverse(inverse(n1)) = n1,
inference(demodulation,[status(thm)],[c_1063,c_1461]) ).
tcf(c_1467,plain,
! [X0: $i] : add(multiply(X0,inverse(X0)),n1) = n1,
inference(superposition,[status(thm)],[c_1461,c_84]) ).
tcf(c_1496,plain,
! [X0: $i] : add(X0,n1) = n1,
inference(superposition,[status(thm)],[c_1467,c_159]) ).
tcf(c_1537,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X0)),X1) = add(inverse(n1),X1),
inference(superposition,[status(thm)],[c_1052,c_1315]) ).
tcf(c_1639,plain,
! [X0: $i] : add(inverse(n1),inverse(multiply(X0,inverse(X0)))) = n1,
inference(superposition,[status(thm)],[c_1537,c_59]) ).
tcf(c_1658,plain,
! [X0: $i] : inverse(multiply(X0,inverse(X0))) = n1,
inference(demodulation,[status(thm)],[c_1639,c_1369]) ).
tcf(c_1672,plain,
! [X0: $i,X1: $i] : add(multiply(X0,n1),multiply(multiply(X1,inverse(X1)),add(X0,n1))) = X0,
inference(superposition,[status(thm)],[c_1658,c_83]) ).
tcf(c_1677,plain,
! [X0: $i,X1: $i] : add(multiply(X0,n1),multiply(multiply(X1,inverse(X1)),n1)) = X0,
inference(light_normalisation,[status(thm)],[c_1672,c_1496]) ).
tcf(c_1969,plain,
! [X0: $i] : add(multiply(X0,n1),multiply(inverse(n1),add(X0,n1))) = X0,
inference(superposition,[status(thm)],[c_1463,c_83]) ).
tcf(c_1971,plain,
! [X0: $i] : add(multiply(X0,n1),multiply(inverse(n1),n1)) = X0,
inference(light_normalisation,[status(thm)],[c_1969,c_1496]) ).
tcf(c_2063,plain,
! [X0: $i] : multiply(n1,add(X0,inverse(n1))) = X0,
inference(demodulation,[status(thm)],[c_1971,c_58]) ).
tcf(c_2064,plain,
! [X0: $i] : multiply(X0,inverse(n1)) = inverse(n1),
inference(demodulation,[status(thm)],[c_1041,c_2063]) ).
tcf(c_2076,plain,
! [X0: $i] : add(multiply(X0,inverse(n1)),X0) = X0,
inference(superposition,[status(thm)],[c_2063,c_83]) ).
tcf(c_2079,plain,
! [X0: $i] : add(inverse(n1),X0) = X0,
inference(light_normalisation,[status(thm)],[c_2076,c_2064]) ).
tcf(c_2084,plain,
! [X0: $i] : multiply(n1,X0) = X0,
inference(demodulation,[status(thm)],[c_1318,c_2079]) ).
tcf(c_2085,plain,
! [X0: $i] : multiply(X0,n1) = X0,
inference(demodulation,[status(thm)],[c_1070,c_2084]) ).
tcf(c_2146,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,n1)) = multiply(n1,add(X0,X1)),
inference(superposition,[status(thm)],[c_2085,c_58]) ).
tcf(c_2428,plain,
! [X0: $i,X1: $i] : add(X0,multiply(multiply(X1,inverse(X1)),n1)) = X0,
inference(light_normalisation,[status(thm)],[c_1677,c_2085]) ).
tcf(c_2429,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X1))) = X0,
inference(demodulation,[status(thm)],[c_2428,c_2084,c_2146]) ).
tcf(c_2445,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = inverse(n1),
inference(superposition,[status(thm)],[c_2429,c_2079]) ).
tcf(c_2452,plain,
multiply(a,inverse(a)) != inverse(n1),
inference(demodulation,[status(thm)],[c_63,c_2445]) ).
tcf(c_2453,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2452,c_2445]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO025-1 : 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 06:35:21 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
% 0.03/0.32
% 0.03/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.32
% 0.03/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 2.33/0.96 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.33/0.96 % SZS status Started for theBenchmark.p
% 2.33/0.96 % SZS status Unsatisfiable for theBenchmark.p
% 2.33/0.96
% 2.33/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.33/0.96
% 2.33/0.96 % ------ iProver source info
% 2.33/0.96
% 2.33/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 2.33/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.33/0.96 % git: non_committed_changes: false
% 2.33/0.96
% 2.33/0.96 % ------ Parsing...% successful
% 2.33/0.96
% 2.33/0.96
% 2.33/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.33/0.96
% 2.33/0.96 % ------ Preprocessing... sup_sim: 3 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.33/0.96
% 2.33/0.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.33/0.96
% 2.33/0.96 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.33/0.96 % ------ Proving...
% 2.33/0.96 % ------ Problem Properties
% 2.33/0.96
% 2.33/0.96 %
% 2.33/0.96 % clauses 7
% 2.33/0.96 % conjectures 1
% 2.33/0.96 % EPR 0
% 2.33/0.96 % Horn 7
% 2.33/0.96 % unary 7
% 2.33/0.96 % binary 0
% 2.33/0.96 % lits 7
% 2.33/0.96 % lits eq 7
% 2.33/0.96 % fd_pure 0
% 2.33/0.96 % fd_pseudo 0
% 2.33/0.96 % fd_cond 0
% 2.33/0.96 % fd_pseudo_cond 0
% 2.33/0.96 % AC symbols 0
% 2.33/0.96
% 2.33/0.96 % ------ Input Options Time Limit: Unbounded
% 2.33/0.96
% 2.33/0.96
% 2.33/0.96 % ------
% 2.33/0.96 % Current options:
% 2.33/0.96 % ------
% 2.33/0.96
% 2.33/0.96
% 2.33/0.96 %
% 2.33/0.96
% 2.33/0.96 % ------ Proving...
% 2.33/0.96 %
% 2.33/0.96
% 2.33/0.96 % SZS status Unsatisfiable for theBenchmark.p
% 2.33/0.96
% 2.33/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/0.96
% 2.33/0.96
%------------------------------------------------------------------------------