%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 02:38:08 PM UTC 2026
% Result : Unsatisfiable 4.89s 1.54s
% Output : CNFRefutation 4.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 35 unt; 0 def)
% Number of atoms : 176 ( 51 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 92 ( 48 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 119 ( 0 sgn 119 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation2) ).
fof(f20,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f21,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f22,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
tcf(c_71,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_76,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X6,X2,X5)
| ~ product(X6,X1,X4)
| ~ product(X6,X0,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X2,X6,X5)
| ~ product(X1,X6,X4)
| ~ product(X0,X6,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_90,plain,
product(a,b,c),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,negated_conjecture,
c != d,
inference(cnf_transformation,[],[f22]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( add(X3,X1) != X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_104,plain,
multiply(a,b) = c,
inference(well_definedness,[status(thm)],[c_90]) ).
tcf(c_105,plain,
multiply(additive_inverse(a),additive_inverse(b)) = d,
inference(well_definedness,[status(thm)],[c_91]) ).
tcf(c_106,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_111,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X5,X1) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X0,X3) != X5 )
| ( multiply(X3,X1) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_85]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_116]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( add(X0,X1) != add(X2,X1) ) ),
inference(unflattening,[status(thm)],[c_102]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_114]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_128]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_124]) ).
tcf(c_330,negated_conjecture,
c != d,
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i] :
( ( X0 = additive_identity )
| ( add(X0,X1) != X1 ) ),
inference(superposition,[status(thm)],[c_106,c_263]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i] : add(multiply(additive_identity,X0),multiply(X1,X0)) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_106,c_275]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = multiply(additive_identity,X1),
inference(superposition,[status(thm)],[c_111,c_275]) ).
tcf(c_691,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_106,c_277]) ).
tcf(c_693,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_111,c_277]) ).
tcf(c_1273,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(superposition,[status(thm)],[c_471,c_414]) ).
tcf(c_1441,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_691,c_414]) ).
tcf(c_1749,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = additive_identity,
inference(demodulation,[status(thm)],[c_473,c_1273]) ).
tcf(c_1750,plain,
add(c,multiply(additive_inverse(a),b)) = additive_identity,
inference(superposition,[status(thm)],[c_104,c_1749]) ).
tcf(c_1919,plain,
! [X0: $i] : add(c,add(multiply(additive_inverse(a),b),X0)) = add(additive_identity,X0),
inference(superposition,[status(thm)],[c_1750,c_273]) ).
tcf(c_1936,plain,
! [X0: $i] : add(c,add(multiply(additive_inverse(a),b),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1919,c_106]) ).
tcf(c_3146,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_693,c_1441]) ).
tcf(c_3186,plain,
multiply(additive_inverse(a),additive_inverse(b)) = add(c,additive_identity),
inference(superposition,[status(thm)],[c_3146,c_1936]) ).
tcf(c_3196,plain,
multiply(additive_inverse(a),additive_inverse(b)) = add(additive_identity,c),
inference(theory_normalisation,[status(thm)],[c_3186,c_273,c_259]) ).
tcf(c_3224,plain,
add(additive_identity,c) = d,
inference(demodulation,[status(thm)],[c_105,c_3196]) ).
tcf(c_3232,plain,
add(additive_identity,c) != c,
inference(demodulation,[status(thm)],[c_330,c_3224]) ).
tcf(c_3233,plain,
$false,
inference(ground_joinability,[status(thm)],[c_3232,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Thu Sep 24 07:39:07 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 0.26/0.52
% 0.26/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.52
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.54 % Proving...
% 4.89/1.54 % SZS status Started for theBenchmark.p
% 4.89/1.54 % SZS status Unsatisfiable for theBenchmark.p
% 4.89/1.54
% 4.89/1.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.89/1.54
% 4.89/1.54 % ------ iProver source info
% 4.89/1.54
% 4.89/1.54 % git: date: 2026-07-19 20:42:38 +0200
% 4.89/1.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.89/1.54 % git: non_committed_changes: false
% 4.89/1.54
% 4.89/1.54 % ------ Parsing...% successful
% 4.89/1.54
% 4.89/1.54
% 4.89/1.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.89/1.54
% 4.89/1.54 % ------ Preprocessing... sup_sim: 17 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.89/1.54
% 4.89/1.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.89/1.54
% 4.89/1.54 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.89/1.54 % ------ Proving...
% 4.89/1.54 % ------ Problem Properties
% 4.89/1.54
% 4.89/1.54 %
% 4.89/1.54 % clauses 13
% 4.89/1.54 % conjectures 1
% 4.89/1.54 % EPR 1
% 4.89/1.54 % Horn 13
% 4.89/1.54 % unary 11
% 4.89/1.54 % binary 2
% 4.89/1.54 % lits 15
% 4.89/1.54 % lits eq 15
% 4.89/1.54 % fd_pure 0
% 4.89/1.54 % fd_pseudo 0
% 4.89/1.54 % fd_cond 0
% 4.89/1.54 % fd_pseudo_cond 2
% 4.89/1.54 % AC symbols 1
% 4.89/1.54
% 4.89/1.54 % ------ Schedule dynamic 5 is on
% 4.89/1.54
% 4.89/1.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.89/1.54
% 4.89/1.54
% 4.89/1.54 % ------
% 4.89/1.54 % Current options:
% 4.89/1.54 % ------
% 4.89/1.54
% 4.89/1.54
% 4.89/1.54 %
% 4.89/1.54
% 4.89/1.54 % ------ Proving...
% 4.89/1.54 %
% 4.89/1.54
% 4.89/1.54 % SZS status Unsatisfiable for theBenchmark.p
% 4.89/1.54
% 4.89/1.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.89/1.54
% 4.89/1.54
%------------------------------------------------------------------------------