%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 01:35:11 PM UTC 2026
% Result : Unsatisfiable 2.73s 1.17s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 111 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f7,axiom,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f8,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tcf(c_57,plain,
! [X0: $i] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,plain,
! [X0: $i] : mult(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_58,c_60]) ).
tcf(c_89,plain,
! [X0: $i] : mult(X0,ld(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_57,c_59]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] : mult(rd(rd(X0,X0),X1),X1) = mult(X0,ld(X0,ld(X1,X1))),
inference(demodulation,[status(thm)],[c_63,c_59,c_60]) ).
tcf(c_91,plain,
mult(ld(x0,x1),ld(ld(x0,x1),x2)) != mult(x0,ld(x0,x2)),
inference(demodulation,[status(thm)],[c_64,c_59]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(demodulation,[status(thm)],[c_62,c_60]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(demodulation,[status(thm)],[c_61,c_59]) ).
tcf(c_156,plain,
! [X0: $i] : mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[c_89,c_59]) ).
tcf(c_159,plain,
! [X0: $i] : mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(superposition,[status(thm)],[c_88,c_60]) ).
tcf(c_160,plain,
! [X0: $i] : mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[c_89,c_60]) ).
tcf(c_167,plain,
! [X0: $i] : ld(X0,X0) = rd(X0,X0),
inference(demodulation,[status(thm)],[c_159,c_90,c_156]) ).
tcf(c_168,plain,
! [X0: $i] : mult(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_88,c_167]) ).
tcf(c_171,plain,
! [X0: $i] : mult(ld(X0,X0),ld(ld(X0,X0),X0)) = ld(ld(X0,X0),X0),
inference(superposition,[status(thm)],[c_168,c_59]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] : mult(rd(ld(X0,X0),X1),X1) = mult(X0,ld(X0,ld(X1,X1))),
inference(light_normalisation,[status(thm)],[c_90,c_167]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
inference(superposition,[status(thm)],[c_89,c_92]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(ld(X0,X0),mult(rd(X0,X2),X2)),
inference(superposition,[status(thm)],[c_168,c_92]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),ld(X1,X1)) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_89,c_93]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_168,c_93]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(X0,ld(X0,ld(X2,X2)))),
inference(demodulation,[status(thm)],[c_183,c_175]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] : mult(rd(X0,ld(X1,X1)),ld(X1,X1)) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(superposition,[status(thm)],[c_167,c_342]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i] : mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = mult(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[c_156,c_342]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i] : mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_353,c_89]) ).
tcf(c_367,plain,
! [X0: $i] : mult(X0,mult(X0,ld(X0,ld(X0,X0)))) = rd(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[c_160,c_349]) ).
tcf(c_368,plain,
! [X0: $i] : rd(X0,ld(X0,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_367,c_89,c_156]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,rd(X2,X0))),rd(X1,rd(X2,X0))) = mult(ld(X0,X0),X0),
inference(superposition,[status(thm)],[c_366,c_186]) ).
tcf(c_644,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,rd(X2,X0))),rd(X1,rd(X2,X0))) = X0,
inference(light_normalisation,[status(thm)],[c_621,c_168]) ).
tcf(c_848,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(superposition,[status(thm)],[c_89,c_212]) ).
tcf(c_875,plain,
! [X0: $i] : ld(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_171,c_848]) ).
tcf(c_954,plain,
! [X0: $i,X1: $i] : mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),ld(X1,X1)) = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[c_875,c_212]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(ld(X0,X1),X2),ld(ld(ld(X0,X1),X2),X0)) = mult(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[c_848,c_212]) ).
tcf(c_1035,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(ld(X0,X1),X2),ld(ld(ld(X0,X1),X2),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1023,c_89]) ).
tcf(c_1073,plain,
! [X0: $i,X1: $i] : mult(rd(ld(X0,X0),rd(X1,X0)),rd(X1,X0)) = ld(X0,X0),
inference(superposition,[status(thm)],[c_368,c_644]) ).
tcf(c_1337,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[c_875,c_1035]) ).
tcf(c_1384,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(rd(X1,X0),rd(X1,X0)))) = ld(X0,X0),
inference(demodulation,[status(thm)],[c_1073,c_175]) ).
tcf(c_1391,plain,
! [X0: $i] : mult(ld(X0,X0),ld(ld(X0,X0),ld(X0,X0))) = ld(ld(X0,X0),ld(X0,X0)),
inference(superposition,[status(thm)],[c_368,c_1384]) ).
tcf(c_1835,plain,
! [X0: $i] : mult(mult(X0,ld(X0,ld(X0,X0))),ld(ld(X0,X0),ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[c_1337,c_212]) ).
tcf(c_1837,plain,
! [X0: $i] : ld(ld(X0,X0),ld(X0,X0)) = ld(X0,X0),
inference(light_normalisation,[status(thm)],[c_1835,c_156,c_1391]) ).
tcf(c_1913,plain,
! [X0: $i,X1: $i] : mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),ld(X1,X1)) = mult(ld(X0,X0),ld(ld(X0,X0),X1)),
inference(superposition,[status(thm)],[c_1837,c_212]) ).
tcf(c_1924,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X0),ld(ld(X0,X0),X1)) = mult(X0,ld(X0,X1)),
inference(light_normalisation,[status(thm)],[c_1913,c_954]) ).
tcf(c_2182,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
inference(superposition,[status(thm)],[c_1924,c_93]) ).
tcf(c_2205,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(ld(X2,X2),X2))),
inference(demodulation,[status(thm)],[c_216,c_2182]) ).
tcf(c_2208,plain,
mult(x0,ld(x0,mult(ld(x2,x2),x2))) != mult(x0,ld(x0,x2)),
inference(demodulation,[status(thm)],[c_91,c_2205]) ).
tcf(c_2209,plain,
$false,
inference(ground_joinability,[status(thm)],[c_2208,c_168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 15:40:56 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running UEQ theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 2.73/1.17 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.73/1.17 % SZS status Started for theBenchmark.p
% 2.73/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 2.73/1.17
% 2.73/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.73/1.17
% 2.73/1.17 % ------ iProver source info
% 2.73/1.17
% 2.73/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.73/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.73/1.17 % git: non_committed_changes: false
% 2.73/1.17
% 2.73/1.17 % ------ Parsing...% successful
% 2.73/1.17
% 2.73/1.17
% 2.73/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.73/1.17
% 2.73/1.17 % ------ Preprocessing... sup_sim: 6 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.73/1.17
% 2.73/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.73/1.17
% 2.73/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.73/1.17 % ------ Proving...
% 2.73/1.17 % ------ Problem Properties
% 2.73/1.17
% 2.73/1.17 %
% 2.73/1.17 % clauses 8
% 2.73/1.17 % conjectures 0
% 2.73/1.17 % EPR 0
% 2.73/1.17 % Horn 8
% 2.73/1.17 % unary 8
% 2.73/1.17 % binary 0
% 2.73/1.17 % lits 8
% 2.73/1.17 % lits eq 8
% 2.73/1.17 % fd_pure 0
% 2.73/1.17 % fd_pseudo 0
% 2.73/1.17 % fd_cond 0
% 2.73/1.17 % fd_pseudo_cond 0
% 2.73/1.17 % AC symbols 0
% 2.73/1.17
% 2.73/1.17 % ------ Input Options Time Limit: Unbounded
% 2.73/1.17
% 2.73/1.17
% 2.73/1.17 % ------
% 2.73/1.17 % Current options:
% 2.73/1.17 % ------
% 2.73/1.17
% 2.73/1.17
% 2.73/1.17 %
% 2.73/1.17
% 2.73/1.17 % ------ Proving...
% 2.73/1.17 %
% 2.73/1.17
% 2.73/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 2.73/1.17
% 2.73/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.73/1.18
% 2.73/1.18
%------------------------------------------------------------------------------