%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP018^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Wed Sep 30 08:07:49 AM UTC 2026
% Result : Theorem 0.21s 0.33s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP018^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:32:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.33 % (2101920)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.33 % (2101929)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4146786932:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.33 % (2101931)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.33 % (2101931)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.33 % (2101926)lrs+10_16_si=on:nwc=1.5:random_seed=2073602323:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.33 % (2101925)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4074903443:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.33 % (2101929)Instruction limit reached!
% 0.21/0.33 % (2101929)------------------------------
% 0.21/0.33 % (2101929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (2101929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (2101929)CaDiCaL version: 2.1.3
% 0.21/0.33 % (2101929)Termination reason: Instruction limit
% 0.21/0.33 % (2101929)Termination phase: Saturation
% 0.21/0.33 % (2101929)Time elapsed: 0.007 s
% 0.21/0.33 % (2101929)Peak memory usage: 12 MB
% 0.21/0.33 % (2101927)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=686772932:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.33 % (2101929)Instructions burned: 24 (million)
% 0.21/0.33 % (2101928)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3707401952:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.33 % (2101931)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2721332673:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.33 % (2101930)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2041264393:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.33 % (2101927)Instruction limit reached!
% 0.21/0.33 % (2101927)------------------------------
% 0.21/0.33 % (2101927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (2101927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (2101927)CaDiCaL version: 2.1.3
% 0.21/0.33 % (2101927)Termination reason: Instruction limit
% 0.21/0.33 % (2101927)Termination phase: Unused predicate definition removal
% 0.21/0.33 % (2101927)Time elapsed: 0.002 s
% 0.21/0.33 % (2101927)Peak memory usage: 10 MB
% 0.21/0.33 % (2101927)Instructions burned: 3 (million)
% 0.21/0.33 % (2101926)Instruction limit reached!
% 0.21/0.33 % (2101926)------------------------------
% 0.21/0.33 % (2101926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (2101926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (2101926)CaDiCaL version: 2.1.3
% 0.21/0.33 % (2101926)Termination reason: Instruction limit
% 0.21/0.33 % (2101926)Termination phase: Saturation
% 0.21/0.33 % (2101926)Time elapsed: 0.011 s
% 0.21/0.33 % (2101926)Peak memory usage: 12 MB
% 0.21/0.33 % (2101926)Instructions burned: 20 (million)
% 0.21/0.33 % (2101939)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1800805691:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.33 % (2101939)Instruction limit reached!
% 0.21/0.33 % (2101939)------------------------------
% 0.21/0.33 % (2101939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (2101939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (2101939)CaDiCaL version: 2.1.3
% 0.21/0.33 % (2101939)Termination reason: Instruction limit
% 0.21/0.33 % (2101939)Termination phase: Saturation
% 0.21/0.33 % (2101939)Time elapsed: 0.004 s
% 0.21/0.33 % (2101939)Peak memory usage: 12 MB
% 0.21/0.33 % (2101939)Instructions burned: 13 (million)
% 0.21/0.33 % (2101940)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1748525389:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.33 % (2101940)Instruction limit reached!
% 0.21/0.33 % (2101940)------------------------------
% 0.21/0.33 % (2101940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (2101940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (2101940)CaDiCaL version: 2.1.3
% 0.21/0.33 % (2101940)Termination reason: Instruction limit
% 0.21/0.33 % (2101940)Termination phase: Property scanning
% 0.21/0.33 % (2101940)Time elapsed: 0.002 s
% 0.21/0.33 % (2101940)Peak memory usage: 10 MB
% 0.21/0.33 % (2101940)Instructions burned: 5 (million)
% 0.21/0.33 % (2101941)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.33 % (2101943)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4243639904:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.33 % (2101943)Instruction limit reached!
% 0.21/0.33 % (2101943)------------------------------
% 0.21/0.33 % (2101943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (2101943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (2101943)CaDiCaL version: 2.1.3
% 0.21/0.33 % (2101943)Termination reason: Instruction limit
% 0.21/0.33 % (2101943)Termination phase: Saturation
% 0.21/0.33 % (2101943)Time elapsed: 0.003 s
% 0.21/0.33 % (2101943)Peak memory usage: 12 MB
% 0.21/0.33 % (2101943)Instructions burned: 12 (million)
% 0.21/0.33 % (2101941)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3575250366:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.33 % (2101930) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2101920-2101930"...
% 0.21/0.33 % (2101941)Instruction limit reached!
% 0.21/0.33 % (2101941)------------------------------
% 0.21/0.33 % (2101941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (2101941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (2101941)CaDiCaL version: 2.1.3
% 0.21/0.33 % (2101941)Termination reason: Instruction limit
% 0.21/0.33 % (2101941)Termination phase: Saturation
% 0.21/0.33 % (2101941)Time elapsed: 0.004 s
% 0.21/0.33 % (2101941)Peak memory usage: 11 MB
% 0.21/0.33 % (2101941)Instructions burned: 7 (million)
% 0.21/0.33 % (2101930)...printing done.
% 0.21/0.33 % (2101930)Refutation found. Thanks to Tanya!
% 0.21/0.33 % SZS status Theorem for theBenchmark
% 0.21/0.33 % SZS output start Proof for theBenchmark
% 0.21/0.33 thf(type_def_5, type, del: $tType).
% 0.21/0.33 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.33 thf(type_def_7, type, tp__ty_2Erealax_2Ereal: $tType).
% 0.21/0.33 thf(func_def_0, type, bool: del).
% 0.21/0.33 thf(func_def_1, type, ind: del).
% 0.21/0.33 thf(func_def_2, type, arr: (del > del > del)).
% 0.21/0.33 thf(func_def_3, type, mem: ($i > del > $o)).
% 0.21/0.33 thf(func_def_4, type, ap: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_5, type, lam: (del > ($i > $i) > $i)).
% 0.21/0.33 thf(func_def_6, type, p: ($i > $o)).
% 0.21/0.33 thf(func_def_7, type, inj__o: ($o > $i)).
% 0.21/0.33 thf(func_def_9, type, ty_2Erealax_2Ereal: del).
% 0.21/0.33 thf(func_def_10, type, inj__ty_2Erealax_2Ereal: (tp__ty_2Erealax_2Ereal > $i)).
% 0.21/0.33 thf(func_def_11, type, surj__ty_2Erealax_2Ereal: ($i > tp__ty_2Erealax_2Ereal)).
% 0.21/0.33 thf(func_def_13, type, fo__c_2Erealax_2Ereal__neg: (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)).
% 0.21/0.33 thf(func_def_14, type, ty_2Ebinary__ieee_2Efloat: (del > del > del)).
% 0.21/0.33 thf(func_def_15, type, c_2Ebinary__ieee_2Efloat__negate: (del > del > $i)).
% 0.21/0.33 thf(func_def_16, type, ty_2Epair_2Eprod: (del > del > del)).
% 0.21/0.33 thf(func_def_17, type, ty_2Ebool_2Eitself: (del > del)).
% 0.21/0.33 thf(func_def_18, type, c_2Ebinary__ieee_2Efloat__plus__min: (del > del > $i)).
% 0.21/0.33 thf(func_def_19, type, c_2Ebinary__ieee_2Efloat__to__real: (del > del > $i)).
% 0.21/0.33 thf(func_def_20, type, c_2Ebool_2Ethe__value: (del > $i)).
% 0.21/0.33 thf(func_def_21, type, c_2Ebinary__ieee_2Eulp: (del > del > $i)).
% 0.21/0.33 thf(func_def_23, type, c_2Emin_2E_3D: (del > $i)).
% 0.21/0.33 thf(func_def_24, type, c_2Ebool_2E_21: (del > $i)).
% 0.21/0.33 thf(func_def_27, type, sK0: (del > ($i > $i) > del > $i)).
% 0.21/0.33 thf(func_def_28, type, sK1: (del > $i > $i)).
% 0.21/0.33 thf(func_def_29, type, sK2: del).
% 0.21/0.33 thf(func_def_30, type, sK3: del).
% 0.21/0.33 thf(func_def_31, type, sK4: ($i > del > $i > $i)).
% 0.21/0.33 thf(func_def_32, type, vNOT: ($o > $o)).
% 0.21/0.33 thf(f4,axiom,(
% 0.21/0.33 ! [X1 : del,X0 : del,X2 : $i] : ((mem @ X2 @ (arr @ X0 @ X1)) => ! [X3 : $i] : ((mem @ X3 @ X0) => (mem @ (ap @ X2 @ X3) @ X1)))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001^2.ax',ap_tp)).
% 0.21/0.33 thf(f10,axiom,(
% 0.21/0.33 ! [X0 : $i] : ((mem @ X0 @ ty_2Erealax_2Ereal) => (X0 = ((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X0)))))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_ty_2Erealax_2Ereal)).
% 0.21/0.33 thf(f14,axiom,(
% 0.21/0.33 ! [X1 : del,X0 : del] : (mem @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X0 @ X1)) @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1)))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__plus__min)).
% 0.21/0.33 thf(f15,axiom,(
% 0.21/0.33 ! [X0 : del,X1 : del] : (mem @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (arr @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1) @ ty_2Erealax_2Ereal))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__to__real)).
% 0.21/0.33 thf(f16,axiom,(
% 0.21/0.33 ! [X0 : del] : (mem @ (c_2Ebool_2Ethe__value @ X0) @ (ty_2Ebool_2Eitself @ X0))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2Ethe__value)).
% 0.21/0.33 thf(f17,axiom,(
% 0.21/0.33 ! [X0 : del,X1 : del] : (mem @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X0 @ X1)) @ ty_2Erealax_2Ereal))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Eulp)).
% 0.21/0.33 thf(f24,axiom,(
% 0.21/0.33 ! [X0 : del,X2 : $i,X1 : del] : ((mem @ X2 @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1)) => (((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X1) @ X2)))) = ((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ X2))))))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Efloat__to__real__negate)).
% 0.21/0.33 thf(f25,axiom,(
% 0.21/0.33 ! [X0 : del,X1 : del] : (((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))) = ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))))))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eulp)).
% 0.21/0.33 thf(f28,conjecture,(
% 0.21/0.33 ! [X0 : del,X1 : del] : (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))))) = ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))))))),
% 0.21/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eneg__ulp)).
% 0.21/0.33 thf(f29,negated_conjecture,(
% 0.21/0.33 ~ ! [X0 : del,X1 : del] : (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))))) = ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))))))),
% 0.21/0.33 inference(negated_conjecture,[status(cth)],[f28])).
% 0.21/0.33 thf(f30,plain,(
% 0.21/0.33 ! [X0 : del,X1 : del] : (mem @ (c_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X0) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X1 @ X0)) @ (ty_2Ebinary__ieee_2Efloat @ X1 @ X0)))),
% 0.21/0.33 inference(rectify,[],[f14])).
% 0.21/0.33 thf(f31,plain,(
% 0.21/0.33 ! [X0 : del,X1 : del] : ($true = ((mem @ (c_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X0) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X1 @ X0)) @ (ty_2Ebinary__ieee_2Efloat @ X1 @ X0)))))),
% 0.21/0.33 inference(fool_elimination,[],[f30])).
% 0.21/0.33 thf(f38,plain,(
% 0.21/0.33 ! [X0 : $i] : ((mem @ X0 @ ty_2Erealax_2Ereal) => (X0 = ((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X0)))))),
% 0.21/0.33 inference(rectify,[],[f10])).
% 0.21/0.33 thf(f39,plain,(
% 0.21/0.33 ! [X0 : $i] : ((((mem @ X0 @ ty_2Erealax_2Ereal)) = $true) => (((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X0))) = X0))),
% 0.21/0.33 inference(fool_elimination,[],[f38])).
% 0.21/0.33 thf(f42,plain,(
% 0.21/0.33 ! [X0 : del] : (mem @ (c_2Ebool_2Ethe__value @ X0) @ (ty_2Ebool_2Eitself @ X0))),
% 0.21/0.33 inference(rectify,[],[f16])).
% 0.21/0.33 thf(f43,plain,(
% 0.21/0.33 ! [X0 : del] : (((mem @ (c_2Ebool_2Ethe__value @ X0) @ (ty_2Ebool_2Eitself @ X0))) = $true)),
% 0.21/0.33 inference(fool_elimination,[],[f42])).
% 0.21/0.33 thf(f50,plain,(
% 0.21/0.33 ! [X0 : del,X1 : $i,X2 : del] : ((mem @ X1 @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X2)) => (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X2) @ X1)))) = ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X2) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X2) @ X1))))))),
% 0.21/0.33 inference(rectify,[],[f24])).
% 0.21/0.33 thf(f51,plain,(
% 0.21/0.33 ! [X1 : $i,X0 : del,X2 : del] : (($true = ((mem @ X1 @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X2)))) => (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X2) @ X1)))) = ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X2) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X2) @ X1))))))),
% 0.21/0.33 inference(fool_elimination,[],[f50])).
% 0.21/0.33 thf(f52,plain,(
% 0.21/0.33 ! [X0 : del,X1 : del,X2 : $i] : ((mem @ X2 @ (arr @ X1 @ X0)) => ! [X3 : $i] : ((mem @ X3 @ X1) => (mem @ (ap @ X2 @ X3) @ X0)))),
% 0.21/0.33 inference(rectify,[],[f4])).
% 0.21/0.33 thf(f53,plain,(
% 0.21/0.33 ! [X2 : $i,X1 : del,X0 : del] : (($true = ((mem @ X2 @ (arr @ X1 @ X0)))) => ! [X3 : $i] : (($true = ((mem @ X3 @ X1))) => ($true = ((mem @ (ap @ X2 @ X3) @ X0)))))),
% 0.21/0.33 inference(fool_elimination,[],[f52])).
% 0.21/0.33 thf(f58,plain,(
% 0.21/0.33 ! [X0 : del,X1 : del] : (mem @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X0 @ X1)) @ ty_2Erealax_2Ereal))),
% 0.21/0.33 inference(rectify,[],[f17])).
% 0.21/0.33 thf(f59,plain,(
% 0.21/0.33 ! [X1 : del,X0 : del] : (((mem @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X0 @ X1)) @ ty_2Erealax_2Ereal))) = $true)),
% 0.21/0.33 inference(fool_elimination,[],[f58])).
% 0.21/0.33 thf(f64,plain,(
% 0.21/0.33 ! [X0 : del,X1 : del] : (mem @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (arr @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1) @ ty_2Erealax_2Ereal))),
% 0.21/0.33 inference(rectify,[],[f15])).
% 0.21/0.33 thf(f65,plain,(
% 0.21/0.33 ! [X1 : del,X0 : del] : (((mem @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (arr @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1) @ ty_2Erealax_2Ereal))) = $true)),
% 0.21/0.33 inference(fool_elimination,[],[f64])).
% 0.21/0.33 thf(f77,plain,(
% 0.21/0.33 ? [X1 : del,X0 : del] : (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))))) != ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))))))),
% 0.21/0.33 inference(ennf_transformation,[],[f29])).
% 0.21/0.33 thf(f83,plain,(
% 0.21/0.33 ! [X0 : $i] : ((((mem @ X0 @ ty_2Erealax_2Ereal)) != $true) | (((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X0))) = X0))),
% 0.21/0.33 inference(ennf_transformation,[],[f39])).
% 0.21/0.33 thf(f84,plain,(
% 0.21/0.33 ! [X2 : del,X0 : del,X1 : $i] : (($true != ((mem @ X1 @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X2)))) | (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X2) @ X1)))) = ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X2) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X2) @ X1))))))),
% 0.21/0.33 inference(ennf_transformation,[],[f51])).
% 0.21/0.33 thf(f85,plain,(
% 0.21/0.33 ! [X0 : del,X2 : $i,X1 : del] : (! [X3 : $i] : (($true != ((mem @ X3 @ X1))) | ($true = ((mem @ (ap @ X2 @ X3) @ X0)))) | ($true != ((mem @ X2 @ (arr @ X1 @ X0)))))),
% 0.21/0.33 inference(ennf_transformation,[],[f53])).
% 0.21/0.33 thf(f88,plain,(
% 0.21/0.33 ! [X0 : del,X1 : del] : ($true = ((mem @ (c_2Ebinary__ieee_2Efloat__to__real @ X1 @ X0) @ (arr @ (ty_2Ebinary__ieee_2Efloat @ X1 @ X0) @ ty_2Erealax_2Ereal))))),
% 0.21/0.33 inference(rectify,[],[f65])).
% 0.21/0.33 thf(f91,plain,(
% 0.21/0.33 ! [X0 : del,X1 : del,X2 : $i] : (($true != ((mem @ X2 @ (ty_2Ebinary__ieee_2Efloat @ X1 @ X0)))) | (((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X1 @ X0) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X1 @ X0) @ X2)))) = ((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X1 @ X0) @ X2))))))),
% 0.21/0.33 inference(rectify,[],[f84])).
% 0.21/0.33 thf(f96,plain,(
% 0.21/0.33 ! [X0 : del,X1 : $i,X2 : del] : (! [X3 : $i] : (($true != ((mem @ X3 @ X2))) | ($true = ((mem @ (ap @ X1 @ X3) @ X0)))) | ($true != ((mem @ X1 @ (arr @ X2 @ X0)))))),
% 0.21/0.33 inference(rectify,[],[f85])).
% 0.21/0.33 thf(f98,plain,(
% 0.21/0.33 ? [X0 : del,X1 : del] : (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Eulp @ X1 @ X0) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X1 @ X0)))))) != ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X1 @ X0) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X1 @ X0) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X0) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X1 @ X0))))))))),
% 0.21/0.33 inference(rectify,[],[f77])).
% 0.21/0.33 thf(f99,plain,(
% 0.21/0.33 (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Eulp @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2)))))) != ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2))))))))),
% 0.21/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f98])).
% 0.21/0.33 thf(f102,plain,(
% 0.21/0.33 ! [X0 : del,X1 : del] : ($true = ((mem @ (c_2Ebinary__ieee_2Eulp @ X1 @ X0) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X1 @ X0)) @ ty_2Erealax_2Ereal))))),
% 0.21/0.33 inference(rectify,[],[f59])).
% 0.21/0.33 thf(f107,plain,(
% 0.21/0.33 ( ! [X0 : del] : ((((mem @ (c_2Ebool_2Ethe__value @ X0) @ (ty_2Ebool_2Eitself @ X0))) = $true)) )),
% 0.21/0.33 inference(cnf_transformation,[],[f43])).
% 0.21/0.33 thf(f109,plain,(
% 0.21/0.33 ( ! [X0 : del,X1 : del] : (($true = ((mem @ (c_2Ebinary__ieee_2Efloat__to__real @ X1 @ X0) @ (arr @ (ty_2Ebinary__ieee_2Efloat @ X1 @ X0) @ ty_2Erealax_2Ereal))))) )),
% 0.21/0.33 inference(cnf_transformation,[],[f88])).
% 0.21/0.33 thf(f112,plain,(
% 0.21/0.33 ( ! [X0 : del,X1 : del] : (($true = ((mem @ (c_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X0) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X1 @ X0)) @ (ty_2Ebinary__ieee_2Efloat @ X1 @ X0)))))) )),
% 0.21/0.33 inference(cnf_transformation,[],[f31])).
% 0.21/0.33 thf(f113,plain,(
% 0.21/0.33 ( ! [X2 : $i,X0 : del,X1 : del] : (($true != ((mem @ X2 @ (ty_2Ebinary__ieee_2Efloat @ X1 @ X0)))) | (((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X1 @ X0) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X1 @ X0) @ X2)))) = ((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X1 @ X0) @ X2)))))) )),
% 0.21/0.33 inference(cnf_transformation,[],[f91])).
% 0.21/0.33 thf(f115,plain,(
% 0.21/0.33 ( ! [X0 : del,X1 : del] : ((((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))) = ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))))))) )),
% 0.21/0.33 inference(cnf_transformation,[],[f25])).
% 0.21/0.33 thf(f122,plain,(
% 0.21/0.33 ( ! [X0 : $i] : ((((mem @ X0 @ ty_2Erealax_2Ereal)) != $true) | (((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X0))) = X0)) )),
% 0.21/0.33 inference(cnf_transformation,[],[f83])).
% 0.21/0.33 thf(f125,plain,(
% 0.21/0.33 ( ! [X2 : del,X3 : $i,X0 : del,X1 : $i] : (($true != ((mem @ X1 @ (arr @ X2 @ X0)))) | ($true != ((mem @ X3 @ X2))) | ($true = ((mem @ (ap @ X1 @ X3) @ X0)))) )),
% 0.21/0.33 inference(cnf_transformation,[],[f96])).
% 0.21/0.33 thf(f128,plain,(
% 0.21/0.33 (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Eulp @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2)))))) != ((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2))))))))),
% 0.21/0.34 inference(cnf_transformation,[],[f99])).
% 0.21/0.34 thf(f133,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : (($true = ((mem @ (c_2Ebinary__ieee_2Eulp @ X1 @ X0) @ (arr @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X1 @ X0)) @ ty_2Erealax_2Ereal))))) )),
% 0.21/0.34 inference(cnf_transformation,[],[f102])).
% 0.21/0.34 thf(f137,definition,(
% 0.21/0.34 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.34 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.34 thf(f155,plain,(
% 0.21/0.34 ( ! [X0 : $i] : (($true != $true) | (((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X0))) = X0) | (((mem @ X0 @ ty_2Erealax_2Ereal)) = $false)) )),
% 0.21/0.34 inference(constrained_superposition,[],[f122,f137])).
% 0.21/0.34 thf(f157,plain,(
% 0.21/0.34 ( ! [X0 : $i] : ((((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X0))) = X0) | (((mem @ X0 @ ty_2Erealax_2Ereal)) = $false)) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f155])).
% 0.21/0.34 thf(f180,plain,(
% 0.21/0.34 ( ! [X2 : $i,X0 : del,X1 : del] : (($true != $true) | ($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ X2) @ ty_2Erealax_2Ereal))) | (((mem @ X2 @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1))) != $true)) )),
% 0.21/0.34 inference(constrained_superposition,[],[f125,f109])).
% 0.21/0.34 thf(f181,plain,(
% 0.21/0.34 ( ! [X2 : $i,X0 : del,X1 : del] : (($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ X2) @ ty_2Erealax_2Ereal))) | ($true != ((mem @ X2 @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X0 @ X1))))) | ($true != $true)) )),
% 0.21/0.34 inference(constrained_superposition,[],[f125,f133])).
% 0.21/0.34 thf(f183,plain,(
% 0.21/0.34 ( ! [X2 : $i,X0 : del,X1 : del] : (($true != $true) | ($true != ((mem @ X2 @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X0 @ X1))))) | ($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ X2) @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1))))) )),
% 0.21/0.34 inference(constrained_superposition,[],[f125,f112])).
% 0.21/0.34 thf(f186,plain,(
% 0.21/0.34 ( ! [X2 : $i,X0 : del,X1 : del] : ((((mem @ X2 @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1))) != $true) | ($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ X2) @ ty_2Erealax_2Ereal)))) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f180])).
% 0.21/0.34 thf(f188,plain,(
% 0.21/0.34 ( ! [X2 : $i,X0 : del,X1 : del] : (($true != ((mem @ X2 @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X0 @ X1))))) | ($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ X2) @ ty_2Erealax_2Ereal)))) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f181])).
% 0.21/0.34 thf(f189,plain,(
% 0.21/0.34 ( ! [X2 : $i,X0 : del,X1 : del] : (($true != ((mem @ X2 @ (ty_2Ebool_2Eitself @ (ty_2Epair_2Eprod @ X0 @ X1))))) | ($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ X2) @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1))))) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f183])).
% 0.21/0.34 thf(f417,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : (($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))) @ ty_2Erealax_2Ereal))) | ($true != $true)) )),
% 0.21/0.34 inference(constrained_superposition,[],[f188,f107])).
% 0.21/0.34 thf(f418,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : (($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))) @ ty_2Erealax_2Ereal)))) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f417])).
% 0.21/0.34 thf(f474,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : (($true != $true) | ($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))) @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1))))) )),
% 0.21/0.34 inference(constrained_superposition,[],[f189,f107])).
% 0.21/0.34 thf(f475,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : (($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))) @ (ty_2Ebinary__ieee_2Efloat @ X0 @ X1))))) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f474])).
% 0.21/0.34 thf(f617,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : ((((ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))) = ((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))))))) | (((mem @ (ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))) @ ty_2Erealax_2Ereal)) = $false)) )),
% 0.21/0.34 inference(constrained_superposition,[],[f157,f115])).
% 0.21/0.34 thf(f620,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : ((((ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))) = ((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))))))) | ($true = $false)) )),
% 0.21/0.34 inference(forward_demodulation,[],[f617,f418])).
% 0.21/0.34 thf(f621,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : ((((ap @ (c_2Ebinary__ieee_2Eulp @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))) = ((inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))))))) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f620])).
% 0.21/0.34 thf(f663,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : (($true != $true) | ($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))) @ ty_2Erealax_2Ereal)))) )),
% 0.21/0.34 inference(constrained_superposition,[],[f186,f475])).
% 0.21/0.34 thf(f664,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : (($true != $true) | (((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))))) = ((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))))))) )),
% 0.21/0.34 inference(constrained_superposition,[],[f113,f475])).
% 0.21/0.34 thf(f665,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : (($true = ((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1)))) @ ty_2Erealax_2Ereal)))) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f663])).
% 0.21/0.34 thf(f667,plain,(
% 0.21/0.34 ( ! [X0 : del,X1 : del] : ((((surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__negate @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))))) = ((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ X0 @ X1) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ X0 @ X1) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ X0 @ X1))))))))) )),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f664])).
% 0.21/0.34 thf(f668,plain,(
% 0.21/0.34 (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Eulp @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2)))))) != ((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2))))))))),
% 0.21/0.34 inference(backward_demodulation,[],[f128,f667])).
% 0.21/0.34 thf(f669,plain,(
% 0.21/0.34 (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2))))))) != ((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2))))))))))),
% 0.21/0.34 inference(forward_demodulation,[],[f668,f621])).
% 0.21/0.34 thf(f670,plain,(
% 0.21/0.34 (((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2)))) @ ty_2Erealax_2Ereal)) = $false) | (((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2))))))) != ((surj__ty_2Erealax_2Ereal @ (ap @ c_2Erealax_2Ereal__neg @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2))))))))),
% 0.21/0.34 inference(constrained_superposition,[],[f669,f157])).
% 0.21/0.34 thf(f671,plain,(
% 0.21/0.34 (((mem @ (ap @ (c_2Ebinary__ieee_2Efloat__to__real @ sK3 @ sK2) @ (ap @ (c_2Ebinary__ieee_2Efloat__plus__min @ sK3 @ sK2) @ (c_2Ebool_2Ethe__value @ (ty_2Epair_2Eprod @ sK3 @ sK2)))) @ ty_2Erealax_2Ereal)) = $false)),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f670])).
% 0.21/0.34 thf(f672,plain,(
% 0.21/0.34 ($true = $false)),
% 0.21/0.34 inference(forward_demodulation,[],[f671,f665])).
% 0.21/0.34 thf(f673,plain,(
% 0.21/0.34 $false),
% 0.21/0.34 inference(trivial_inequality_removal,[],[f672])).
% 0.21/0.34 % SZS output end Proof for theBenchmark
% 0.21/0.34 % (2101930)------------------------------
% 0.21/0.34 % (2101930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (2101930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (2101930)CaDiCaL version: 2.1.3
% 0.21/0.34 % (2101930)Termination reason: Refutation
% 0.21/0.34 % (2101930)Time elapsed: 0.036 s
% 0.21/0.34 % (2101930)Peak memory usage: 12 MB
% 0.21/0.34 % (2101930)Instructions burned: 67 (million)
% 0.21/0.34 % (2101920)Success in time 0.086 s
% 0.21/0.34 % Vampire exiting
%------------------------------------------------------------------------------